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ODE</title> <meta name="description" content="Search results for: Nonlinear ODE"> <meta name="keywords" content="Nonlinear ODE"> <meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1, maximum-scale=1, user-scalable=no"> <meta charset="utf-8"> <link href="https://cdn.waset.org/favicon.ico" type="image/x-icon" rel="shortcut icon"> <link href="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/css/bootstrap.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/plugins/fontawesome/css/all.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/css/site.css?v=150220211555" rel="stylesheet"> </head> <body> <header> <div class="container"> <nav class="navbar navbar-expand-lg navbar-light"> <a class="navbar-brand" href="https://waset.org"> <img src="https://cdn.waset.org/static/images/wasetc.png" alt="Open Science Research Excellence" title="Open Science Research Excellence" /> </a> <button class="d-block d-lg-none navbar-toggler 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class="input-group"> <i class="fas fa-search"></i> <input type="text" class="search-query" name="q" placeholder="Author, Title, Abstract, Keywords" value="Nonlinear ODE"> <input type="submit" class="btn_search" value="Search"> </div> </div> </form> </div> </div> <div class="row mt-3"> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Commenced</strong> in January 2007</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Frequency:</strong> Monthly</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Edition:</strong> International</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Paper Count:</strong> 1065</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: Nonlinear ODE</h1> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1065</span> A New Nonlinear PID Controller and its Parameter Design</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Yongping%20Ren">Yongping Ren</a>, <a href="https://publications.waset.org/search?q=Zongli%20Li"> Zongli Li</a>, <a href="https://publications.waset.org/search?q=Fan%20Zhang"> Fan Zhang</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A new nonlinear PID controller and its stability analysis are presented in this paper. A nonlinear function is deduced from the similarities between the control effort and the electric-field effect of a capacitor. The conventional linear PID controller can be modified into a nonlinear one by this function. To analyze the stability of the nonlinear PID controlled system, an idea of energy equivalence is adapted to avoid the conservativeness which is usually arisen from some traditional theorems and Criterions. The energy equivalence is naturally related with the conceptions of Passivity and T-Passivity. As a result, an engineering guideline for the parameter design of the nonlinear PID controller is obtained. An inverted pendulum system is tested to verify the nonlinear PID control scheme. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Nonlinear%20PID%20controller" title="Nonlinear PID controller">Nonlinear PID controller</a>, <a href="https://publications.waset.org/search?q=stability" title=" stability"> stability</a>, <a href="https://publications.waset.org/search?q=gain%20equivalence" title=" gain equivalence"> gain equivalence</a>, <a href="https://publications.waset.org/search?q=dissipative" title="dissipative">dissipative</a>, <a href="https://publications.waset.org/search?q=T-Passivity." title=" T-Passivity."> T-Passivity.</a> </p> <a href="https://publications.waset.org/5321/a-new-nonlinear-pid-controller-and-its-parameter-design" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/5321/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/5321/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/5321/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/5321/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/5321/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/5321/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/5321/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/5321/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/5321/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/5321/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/5321.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">3176</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1064</span> Design of Nonlinear Observer by Using Chebyshev Interpolation based on Formal Linearization</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Kazuo%20Komatsu">Kazuo Komatsu</a>, <a href="https://publications.waset.org/search?q=Hitoshi%20Takata"> Hitoshi Takata</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper discusses a design of nonlinear observer by a formal linearization method using an application of Chebyshev Interpolation in order to facilitate processes for synthesizing a nonlinear observer and to improve the precision of linearization. A dynamic nonlinear system is linearized with respect to a linearization function, and a measurement equation is transformed into an augmented linear one by the formal linearization method which is based on Chebyshev interpolation. To the linearized system, a linear estimation theory is applied and a nonlinear observer is derived. To show effectiveness of the observer design, numerical experiments are illustrated and they indicate that the design shows remarkable performances for nonlinear systems. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=nonlinear%20system" title="nonlinear system">nonlinear system</a>, <a href="https://publications.waset.org/search?q=nonlinear%20observer" title=" nonlinear observer"> nonlinear observer</a>, <a href="https://publications.waset.org/search?q=formal%20linearization" title=" formal linearization"> formal linearization</a>, <a href="https://publications.waset.org/search?q=Chebyshev%20interpolation." title="Chebyshev interpolation.">Chebyshev interpolation.</a> </p> <a href="https://publications.waset.org/3847/design-of-nonlinear-observer-by-using-chebyshev-interpolation-based-on-formal-linearization" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/3847/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/3847/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/3847/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/3847/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/3847/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/3847/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/3847/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/3847/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/3847/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/3847/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/3847.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1594</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1063</span> A NonLinear Observer of an Electrical Transformer: A Bond Graph Approach</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Gilberto%20Gonzalez-A">Gilberto Gonzalez-A </a>, <a href="https://publications.waset.org/search?q=Israel%20Nu%C3%B1ez"> Israel Nu帽ez</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A bond graph model of an electrical transformer including the nonlinear saturation is presented. A nonlinear observer for the transformer based on multivariable circle criterion in the physical domain is proposed. In order to show the saturation and hysteresis effects on the electrical transformer, simulation results are obtained. Finally, the paper describes that convergence of the estimates to the true states is achieved. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Bond%20graph" title="Bond graph">Bond graph</a>, <a href="https://publications.waset.org/search?q=nonlinear%20observer" title=" nonlinear observer"> nonlinear observer</a>, <a href="https://publications.waset.org/search?q=electrical%20transformer" title=" electrical transformer"> electrical transformer</a>, <a href="https://publications.waset.org/search?q=nonlinear%20saturation." title=" nonlinear saturation."> nonlinear saturation.</a> </p> <a href="https://publications.waset.org/15388/a-nonlinear-observer-of-an-electrical-transformer-a-bond-graph-approach" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/15388/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/15388/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/15388/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/15388/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/15388/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/15388/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/15388/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/15388/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/15388/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/15388/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/15388.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1617</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1062</span> Design and Instrumentation of a Benchmark Multivariable Nonlinear Control Laboratory</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=S.%20H.%20Teh">S. H. Teh</a>, <a href="https://publications.waset.org/search?q=S.%20Malawaraarachci"> S. Malawaraarachci</a>, <a href="https://publications.waset.org/search?q=W.%20P.%20Chan"> W. P. Chan</a>, <a href="https://publications.waset.org/search?q=A.%20Nassirharand"> A. Nassirharand</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The purpose of this paper is to present the design and instrumentation of a new benchmark multivariable nonlinear control laboratory. The mathematical model of this system may be used to test the applicability and performance of various nonlinear control procedures. The system is a two degree-of-freedom robotic arm with soft and hard (discontinuous) nonlinear terms. Two novel mechanisms are designed to allow the implementation of adjustable Coulomb friction and backlash. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Nonlinear%20control" title="Nonlinear control">Nonlinear control</a>, <a href="https://publications.waset.org/search?q=describing%20functions" title=" describing functions"> describing functions</a>, <a href="https://publications.waset.org/search?q=AdjustableCoulomb%20friction" title=" AdjustableCoulomb friction"> AdjustableCoulomb friction</a>, <a href="https://publications.waset.org/search?q=Adjustable%20backlash." title=" Adjustable backlash."> Adjustable backlash.</a> </p> <a href="https://publications.waset.org/15520/design-and-instrumentation-of-a-benchmark-multivariable-nonlinear-control-laboratory" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/15520/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/15520/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/15520/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/15520/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/15520/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/15520/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/15520/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/15520/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/15520/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/15520/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/15520.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1856</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1061</span> Robust Adaptive Observer Design for Lipschitz Class of Nonlinear Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=M.%20Pourgholi">M. Pourgholi</a>, <a href="https://publications.waset.org/search?q=V.J.Majd"> V.J.Majd</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>This paper addresses parameter and state estimation problem in the presence of the perturbation of observer gain bounded input disturbances for the Lipschitz systems that are linear in unknown parameters and nonlinear in states. A new nonlinear adaptive resilient observer is designed, and its stability conditions based on Lyapunov technique are derived. The gain for this observer is derived systematically using linear matrix inequality approach. A numerical example is provided in which the nonlinear terms depend on unmeasured states. The simulation results are presented to show the effectiveness of the proposed method.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Adaptive%20observer" title="Adaptive observer">Adaptive observer</a>, <a href="https://publications.waset.org/search?q=linear%20matrix%20inequality" title=" linear matrix inequality"> linear matrix inequality</a>, <a href="https://publications.waset.org/search?q=nonlinear%20systems" title=" nonlinear systems"> nonlinear systems</a>, <a href="https://publications.waset.org/search?q=nonlinear%20observer" title=" nonlinear observer"> nonlinear observer</a>, <a href="https://publications.waset.org/search?q=resilient%20observer" title=" resilient observer"> resilient observer</a>, <a href="https://publications.waset.org/search?q=robust%20estimation." title=" robust estimation."> robust estimation.</a> </p> <a href="https://publications.waset.org/5835/robust-adaptive-observer-design-for-lipschitz-class-of-nonlinear-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/5835/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/5835/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/5835/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/5835/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/5835/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/5835/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/5835/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/5835/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/5835/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/5835/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/5835.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">2613</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1060</span> On the outlier Detection in Nonlinear Regression</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Hossein%20Riazoshams">Hossein Riazoshams</a>, <a href="https://publications.waset.org/search?q=Midi%20Habshah"> Midi Habshah</a>, <a href="https://publications.waset.org/search?q=Jr."> Jr.</a>, <a href="https://publications.waset.org/search?q=Mohamad%20Bakri%20Adam"> Mohamad Bakri Adam</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The detection of outliers is very essential because of their responsibility for producing huge interpretative problem in linear as well as in nonlinear regression analysis. Much work has been accomplished on the identification of outlier in linear regression, but not in nonlinear regression. In this article we propose several outlier detection techniques for nonlinear regression. The main idea is to use the linear approximation of a nonlinear model and consider the gradient as the design matrix. Subsequently, the detection techniques are formulated. Six detection measures are developed that combined with three estimation techniques such as the Least-Squares, M and MM-estimators. The study shows that among the six measures, only the studentized residual and Cook Distance which combined with the MM estimator, consistently capable of identifying the correct outliers. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Nonlinear%20Regression" title="Nonlinear Regression">Nonlinear Regression</a>, <a href="https://publications.waset.org/search?q=outliers" title=" outliers"> outliers</a>, <a href="https://publications.waset.org/search?q=Gradient" title=" Gradient"> Gradient</a>, <a href="https://publications.waset.org/search?q=LeastSquare" title=" LeastSquare"> LeastSquare</a>, <a href="https://publications.waset.org/search?q=M-estimate" title=" M-estimate"> M-estimate</a>, <a href="https://publications.waset.org/search?q=MM-estimate." title=" MM-estimate."> MM-estimate.</a> </p> <a href="https://publications.waset.org/9291/on-the-outlier-detection-in-nonlinear-regression" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/9291/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/9291/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/9291/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/9291/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/9291/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/9291/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/9291/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/9291/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/9291/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/9291/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/9291.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">3179</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1059</span> Solitons in Nonlinear Optical Lattices</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Tapas%20Kumar%20Sinha">Tapas Kumar Sinha</a>, <a href="https://publications.waset.org/search?q=Joseph%20Mathew"> Joseph Mathew</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Based on the Lagrangian for the Gross 鈥揚itaevskii equation as derived by H. Sakaguchi and B.A Malomed [5] we have derived a double well model for the nonlinear optical lattice. This model explains the various features of nonlinear optical lattices. Further, from this model we obtain and simulate the probability for tunneling from one well to another which agrees with experimental results [4]. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Double%20well%20model" title="Double well model">Double well model</a>, <a href="https://publications.waset.org/search?q=nonlinear%20optical%20lattice" title=" nonlinear optical lattice"> nonlinear optical lattice</a>, <a href="https://publications.waset.org/search?q=Solitons" title=" Solitons"> Solitons</a>, <a href="https://publications.waset.org/search?q=tunneling." title=" tunneling."> tunneling.</a> </p> <a href="https://publications.waset.org/5260/solitons-in-nonlinear-optical-lattices" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/5260/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/5260/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/5260/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/5260/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/5260/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/5260/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/5260/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/5260/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/5260/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/5260/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/5260.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1520</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1058</span> On a New Nonlinear Sum-difference Inequality with Application</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Kelong%20Zheng">Kelong Zheng</a>, <a href="https://publications.waset.org/search?q=Shouming%20Zhong"> Shouming Zhong</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A new nonlinear sum-difference inequality in two variables which generalize some existing results and can be used as handy tools in the analysis of certain partial difference equation is discussed. An example to show boundedness of solutions of a difference value problem is also given. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Sum-Difference%20inequality" title="Sum-Difference inequality">Sum-Difference inequality</a>, <a href="https://publications.waset.org/search?q=Nonlinear" title=" Nonlinear"> Nonlinear</a>, <a href="https://publications.waset.org/search?q=Boundedness." title=" Boundedness."> Boundedness.</a> </p> <a href="https://publications.waset.org/1144/on-a-new-nonlinear-sum-difference-inequality-with-application" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/1144/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/1144/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/1144/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/1144/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/1144/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/1144/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/1144/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/1144/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/1144/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/1144/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/1144.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1131</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1057</span> Chaotic Oscillations of Diaphragm Supported by Nonlinear Springs with Hysteresis</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=M.%20Sasajima">M. Sasajima</a>, <a href="https://publications.waset.org/search?q=T.%20Yamaguchi"> T. Yamaguchi</a>, <a href="https://publications.waset.org/search?q=Y.%20Koike"> Y. Koike</a>, <a href="https://publications.waset.org/search?q=A.%20Hara"> A. Hara</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper describes vibration analysis using the finite element method for a small earphone, especially for the diaphragm shape with a low-rigidity. The viscoelastic diaphragm is supported by multiple nonlinear concentrated springs with linear hysteresis damping. The restoring forces of the nonlinear springs have cubic nonlinearity. The finite elements for the nonlinear springs with hysteresis are expressed and are connected to the diaphragm that is modeled by linear solid finite elements in consideration of a complex modulus of elasticity. Further, the discretized equations in physical coordinates are transformed into the nonlinear ordinary coupled equations using normal coordinates corresponding to the linear natural modes. We computed the nonlinear stationary and non-stationary responses due to the internal resonance between modes with large amplitude in the nonlinear springs and elastic modes in the diaphragm. The non-stationary motions are confirmed as the chaos due to the maximum Lyapunov exponents with a positive number. From the time histories of the deformation distribution in the chaotic vibration, we identified nonlinear modal couplings. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Nonlinear%20Vibration" title="Nonlinear Vibration">Nonlinear Vibration</a>, <a href="https://publications.waset.org/search?q=Finite%20Element%20Method" title=" Finite Element Method"> Finite Element Method</a>, <a href="https://publications.waset.org/search?q=Chaos" title="Chaos ">Chaos </a>, <a href="https://publications.waset.org/search?q=Small%20Earphone." title="Small Earphone.">Small Earphone.</a> </p> <a href="https://publications.waset.org/1556/chaotic-oscillations-of-diaphragm-supported-by-nonlinear-springs-with-hysteresis" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/1556/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/1556/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/1556/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/1556/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/1556/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/1556/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/1556/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/1556/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/1556/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/1556/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/1556.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1783</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1056</span> Nonlinear Impact Responses for a Damped Frame Supported by Nonlinear Springs with Hysteresis Using Fast FEA</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=T.%20Yamaguchi">T. Yamaguchi</a>, <a href="https://publications.waset.org/search?q=M.%20Watanabe"> M. Watanabe</a>, <a href="https://publications.waset.org/search?q=M.%20Sasajima"> M. Sasajima</a>, <a href="https://publications.waset.org/search?q=C.%20Yuan"> C. Yuan</a>, <a href="https://publications.waset.org/search?q=S.%20Maruyama"> S. Maruyama</a>, <a href="https://publications.waset.org/search?q=T.%20B.%20Ibrahim"> T. B. Ibrahim</a>, <a href="https://publications.waset.org/search?q=H.%20Tomita"> H. Tomita</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper deals with nonlinear vibration analysis using finite element method for frame structures consisting of elastic and viscoelastic damping layers supported by multiple nonlinear concentrated springs with hysteresis damping. The frame is supported by four nonlinear concentrated springs near the four corners. The restoring forces of the springs have cubic non-linearity and linear component of the nonlinear springs has complex quantity to represent linear hysteresis damping. The damping layer of the frame structures has complex modulus of elasticity. Further, the discretized equations in physical coordinate are transformed into the nonlinear ordinary coupled differential equations using normal coordinate corresponding to linear natural modes. Comparing shares of strain energy of the elastic frame, the damping layer and the springs, we evaluate the influences of the damping couplings on the linear and nonlinear impact responses. We also investigate influences of damping changed by stiffness of the elastic frame on the nonlinear coupling in the damped impact responses. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Dynamic%20response" title="Dynamic response">Dynamic response</a>, <a href="https://publications.waset.org/search?q=Nonlinear%20impact%20response" title=" Nonlinear impact response"> Nonlinear impact response</a>, <a href="https://publications.waset.org/search?q=Finite%0D%0AElement%20analysis" title=" Finite Element analysis"> Finite Element analysis</a>, <a href="https://publications.waset.org/search?q=Numerical%20analysis." title=" Numerical analysis."> Numerical analysis.</a> </p> <a href="https://publications.waset.org/10002251/nonlinear-impact-responses-for-a-damped-frame-supported-by-nonlinear-springs-with-hysteresis-using-fast-fea" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10002251/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10002251/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10002251/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10002251/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10002251/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10002251/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10002251/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10002251/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10002251/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10002251/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10002251.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1720</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1055</span> Observers Design for Systems Modelled by Bond Graphs with Multivariable Monotone Nonlinearities</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Gilberto%20Gonzalez-A">Gilberto Gonzalez-A</a>, <a href="https://publications.waset.org/search?q=Gerardo%20Jaimes-A"> Gerardo Jaimes-A</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A methodology to design a nonlinear observer in a bond graph approach is proposed. The class of nonlinear observer with multivariable nonlinearities is considered. A junction structure of the bond graph observer is proposed. The proposed methodology to an electrical transformer and a DC motor including the nonlinear saturation is applied. Nonlinear observers for the transformer and DC motor based on multivariable circle criterion in the physical domain are proposed. In order to show the saturation effects on the transformer and DC motor, simulation results are obtained. Finally, the paper describes that convergence of the estimates to the true states is achieved. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Bond%20graph" title="Bond graph">Bond graph</a>, <a href="https://publications.waset.org/search?q=nonlinear%20observer" title=" nonlinear observer"> nonlinear observer</a>, <a href="https://publications.waset.org/search?q=electrical%0Atransformer" title=" electrical transformer"> electrical transformer</a>, <a href="https://publications.waset.org/search?q=nonlinear%20saturation" title=" nonlinear saturation"> nonlinear saturation</a> </p> <a href="https://publications.waset.org/8422/observers-design-for-systems-modelled-by-bond-graphs-with-multivariable-monotone-nonlinearities" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/8422/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/8422/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/8422/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/8422/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/8422/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/8422/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/8422/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/8422/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/8422/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/8422/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/8422.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1454</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1054</span> A Model-following Adaptive Controller for Linear/Nonlinear Plantsusing Radial Basis Function Neural Networks</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Yuichi%20Masukake">Yuichi Masukake</a>, <a href="https://publications.waset.org/search?q=Yoshihisa%20Ishida"> Yoshihisa Ishida</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we proposed a method to design a model-following adaptive controller for linear/nonlinear plants. Radial basis function neural networks (RBF-NNs), which are known for their stable learning capability and fast training, are used to identify linear/nonlinear plants. Simulation results show that the proposed method is effective in controlling both linear and nonlinear plants with disturbance in the plant input. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Linear%2Fnonlinear%20plants" title="Linear/nonlinear plants">Linear/nonlinear plants</a>, <a href="https://publications.waset.org/search?q=neural%20networks" title=" neural networks"> neural networks</a>, <a href="https://publications.waset.org/search?q=radial%20basisfunction%20networks." title=" radial basisfunction networks."> radial basisfunction networks.</a> </p> <a href="https://publications.waset.org/6706/a-model-following-adaptive-controller-for-linearnonlinear-plantsusing-radial-basis-function-neural-networks" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/6706/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/6706/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/6706/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/6706/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/6706/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/6706/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/6706/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/6706/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/6706/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/6706/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/6706.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1482</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1053</span> Feedback Stabilization Based on Observer and Guaranteed Cost Control for Lipschitz Nonlinear Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=A.%20Thabet">A. Thabet</a>, <a href="https://publications.waset.org/search?q=G.%20B.%20H.%20Frej"> G. B. H. Frej</a>, <a href="https://publications.waset.org/search?q=M.%20Boutayeb"> M. Boutayeb</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper presents a design of dynamic feedback control based on observer for a class of large scale Lipschitz nonlinear systems. The use of Differential Mean Value Theorem (DMVT) is to introduce a general condition on the nonlinear functions. To ensure asymptotic stability, sufficient conditions are expressed in terms of linear matrix inequalities (LMIs). High performances are shown through real time implementation with ARDUINO Duemilanove board to the one-link flexible joint robot. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Feedback%20stabilization" title="Feedback stabilization">Feedback stabilization</a>, <a href="https://publications.waset.org/search?q=DMVT" title=" DMVT"> DMVT</a>, <a href="https://publications.waset.org/search?q=Lipschitz%20nonlinear%0D%0Asystems" title=" Lipschitz nonlinear systems"> Lipschitz nonlinear systems</a>, <a href="https://publications.waset.org/search?q=nonlinear%20observer" title=" nonlinear observer"> nonlinear observer</a>, <a href="https://publications.waset.org/search?q=real%20time%20implementation." title=" real time implementation."> real time implementation.</a> </p> <a href="https://publications.waset.org/10005575/feedback-stabilization-based-on-observer-and-guaranteed-cost-control-for-lipschitz-nonlinear-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10005575/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10005575/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10005575/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10005575/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10005575/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10005575/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10005575/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10005575/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10005575/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10005575/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10005575.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1361</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1052</span> An Approach to Control Design for Nonlinear Systems via Two-stage Formal Linearization and Two-type LQ Controls</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Kazuo%20Komatsu">Kazuo Komatsu</a>, <a href="https://publications.waset.org/search?q=Hitoshi%20Takata"> Hitoshi Takata</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper we consider a nonlinear control design for nonlinear systems by using two-stage formal linearization and twotype LQ controls. The ordinary LQ control is designed on almost linear region around the steady state point. On the other region, another control is derived as follows. This derivation is based on coordinate transformation twice with respect to linearization functions which are defined by polynomials. The linearized systems can be made up by using Taylor expansion considered up to the higher order. To the resulting formal linear system, the LQ control theory is applied to obtain another LQ control. Finally these two-type LQ controls are smoothly united to form a single nonlinear control. Numerical experiments indicate that this control show remarkable performances for a nonlinear system. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Formal%20Linearization" title="Formal Linearization">Formal Linearization</a>, <a href="https://publications.waset.org/search?q=LQ%20Control" title=" LQ Control"> LQ Control</a>, <a href="https://publications.waset.org/search?q=Nonlinear%20Control" title=" Nonlinear Control"> Nonlinear Control</a>, <a href="https://publications.waset.org/search?q=Taylor%20Expansion" title="Taylor Expansion">Taylor Expansion</a>, <a href="https://publications.waset.org/search?q=Zero%20Function." title=" Zero Function."> Zero Function.</a> </p> <a href="https://publications.waset.org/12695/an-approach-to-control-design-for-nonlinear-systems-via-two-stage-formal-linearization-and-two-type-lq-controls" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/12695/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/12695/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/12695/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/12695/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/12695/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/12695/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/12695/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/12695/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/12695/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/12695/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/12695.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1618</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1051</span> Design of Nonlinear Observer by Using Augmented Linear System based on Formal Linearization of Polynomial Type</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Kazuo%20Komatsu">Kazuo Komatsu</a>, <a href="https://publications.waset.org/search?q=Hitoshi%20Takata"> Hitoshi Takata</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>The objective of this study is to propose an observer design for nonlinear systems by using an augmented linear system derived by application of a formal linearization method. A given nonlinear differential equation is linearized by the formal linearization method which is based on Taylor expansion considering up to the higher order terms, and a measurement equation is transformed into an augmented linear one. To this augmented dimensional linear system, a linear estimation theory is applied and a nonlinear observer is derived. As an application of this method, an estimation problem of transient state of electric power systems is studied, and its numerical experiments indicate that this observer design shows remarkable performances for nonlinear systems.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=nonlinear%20system" title="nonlinear system">nonlinear system</a>, <a href="https://publications.waset.org/search?q=augmented%20linear%20system" title=" augmented linear system"> augmented linear system</a>, <a href="https://publications.waset.org/search?q=nonlinear%20observer" title=" nonlinear observer"> nonlinear observer</a>, <a href="https://publications.waset.org/search?q=formal%20linearization" title=" formal linearization"> formal linearization</a>, <a href="https://publications.waset.org/search?q=electric%20power%20system." title=" electric power system."> electric power system.</a> </p> <a href="https://publications.waset.org/724/design-of-nonlinear-observer-by-using-augmented-linear-system-based-on-formal-linearization-of-polynomial-type" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/724/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/724/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/724/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/724/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/724/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/724/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/724/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/724/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/724/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/724/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/724.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1583</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1050</span> Partial Stabilization of a Class of Nonlinear Systems Via Center Manifold Theory</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Ping%20He">Ping He</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper addresses the problem of the partial state feedback stabilization of a class of nonlinear systems. In order to stabilization this class systems, the especial place of this paper is to reverse designing the state feedback control law from the method of judging system stability with the center manifold theory. First of all, the center manifold theory is applied to discuss the stabilization sufficient condition and design the stabilizing state control laws for a class of nonlinear. Secondly, the problem of partial stabilization for a class of plane nonlinear system is discuss using the lyapunov second method and the center manifold theory. Thirdly, we investigate specially the problem of the stabilization for a class of homogenous plane nonlinear systems, a class of nonlinear with dual-zero eigenvalues and a class of nonlinear with zero-center using the method of lyapunov function with homogenous derivative, specifically. At the end of this paper, some examples and simulation results are given show that the approach of this paper to this class of nonlinear system is effective and convenient. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Partial%20stabilization" title="Partial stabilization">Partial stabilization</a>, <a href="https://publications.waset.org/search?q=Nonlinear%20critical%20systems" title=" Nonlinear critical systems"> Nonlinear critical systems</a>, <a href="https://publications.waset.org/search?q=Centermanifold%20theory" title=" Centermanifold theory"> Centermanifold theory</a>, <a href="https://publications.waset.org/search?q=Lyapunov%20function" title=" Lyapunov function"> Lyapunov function</a>, <a href="https://publications.waset.org/search?q=System%20reduction." title=" System reduction."> System reduction.</a> </p> <a href="https://publications.waset.org/580/partial-stabilization-of-a-class-of-nonlinear-systems-via-center-manifold-theory" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/580/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/580/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/580/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/580/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/580/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/580/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/580/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/580/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/580/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/580/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/580.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1763</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1049</span> The Finite Difference Scheme for the Suspended String Equation with the Nonlinear Damping Term</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Jaipong%20Kasemsuwan">Jaipong Kasemsuwan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A numerical solution of the initial boundary value problem of the suspended string vibrating equation with the particular nonlinear damping term based on the finite difference scheme is presented in this paper. The investigation of how the second and third power terms of the nonlinear term affect the vibration characteristic. We compare the vibration amplitude as a result of the third power nonlinear damping with the second power obtained from previous report provided that the same initial shape and initial velocities are assumed. The comparison results show that the vibration amplitude is inversely proportional to the coefficient of the damping term for the third power nonlinear damping case, while the vibration amplitude is proportional to the coefficient of the damping term in the second power nonlinear damping case. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Finite-difference%20method" title="Finite-difference method">Finite-difference method</a>, <a href="https://publications.waset.org/search?q=the%20nonlinear%20damped%0Aequation" title=" the nonlinear damped equation"> the nonlinear damped equation</a>, <a href="https://publications.waset.org/search?q=the%20numerical%20simulation" title=" the numerical simulation"> the numerical simulation</a>, <a href="https://publications.waset.org/search?q=the%20suspended%20string%20equation" title=" the suspended string equation"> the suspended string equation</a> </p> <a href="https://publications.waset.org/10713/the-finite-difference-scheme-for-the-suspended-string-equation-with-the-nonlinear-damping-term" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10713/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10713/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10713/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10713/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10713/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10713/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10713/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10713/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10713/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10713/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10713.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1451</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1048</span> Direct Design of Steel Bridge Using Nonlinear Inelastic Analysis</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Boo-Sung%20Koh">Boo-Sung Koh</a>, <a href="https://publications.waset.org/search?q=Seung-Eock%20Kim"> Seung-Eock Kim</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper, a direct design using a nonlinear inelastic analysis is suggested. Also, this paper compares the load carrying capacity obtained by a nonlinear inelastic analysis with experiment results to verify the accuracy of the results. The allowable stress design results of a railroad through a plate girder bridge and the safety factor of the nonlinear inelastic analysis were compared to examine the safety performance. As a result, the load safety factor for the nonlinear inelastic analysis was twice as high as the required safety factor under the allowable stress design standard specified in the civil engineering structure design standards for urban magnetic levitation railways, which further verified the advantages of the proposed direct design method.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Direct%20design" title="Direct design">Direct design</a>, <a href="https://publications.waset.org/search?q=nonlinear%20inelastic%20analysis" title=" nonlinear inelastic analysis"> nonlinear inelastic analysis</a>, <a href="https://publications.waset.org/search?q=residual%20stress" title=" residual stress"> residual stress</a>, <a href="https://publications.waset.org/search?q=initial%20geometric%20imperfection." title=" initial geometric imperfection."> initial geometric imperfection.</a> </p> <a href="https://publications.waset.org/10006070/direct-design-of-steel-bridge-using-nonlinear-inelastic-analysis" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10006070/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10006070/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10006070/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10006070/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10006070/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10006070/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10006070/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10006070/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10006070/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10006070/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10006070.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1454</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1047</span> Nonlinear Time-History Analysis of 3-Dimensional Semi-rigid Steel Frames</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Phu-Cuong%20Nguyen">Phu-Cuong Nguyen</a>, <a href="https://publications.waset.org/search?q=Seung-Eock%20Kim"> Seung-Eock Kim</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper presents nonlinear elastic dynamic analysis of 3-D semi-rigid steel frames including geometric and connection nonlinearities. The geometric nonlinearity is considered by using stability functions and updating geometric stiffness matrix. The nonlinear behavior of the steel beam-to-column connection is considered by using a zero-length independent connection element comprising of six translational and rotational springs. The nonlinear dynamic equilibrium equations are solved by the Newmark numerical integration method. The nonlinear time-history analysis results are compared with those of previous studies and commercial SAP2000 software to verify the accuracy and efficiency of the proposed procedure. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Geometric%20nonlinearity" title="Geometric nonlinearity">Geometric nonlinearity</a>, <a href="https://publications.waset.org/search?q=nonlinear%20time-historyanalysis" title=" nonlinear time-historyanalysis"> nonlinear time-historyanalysis</a>, <a href="https://publications.waset.org/search?q=semi-rigid%20connection" title=" semi-rigid connection"> semi-rigid connection</a>, <a href="https://publications.waset.org/search?q=stability%20functions." title=" stability functions."> stability functions.</a> </p> <a href="https://publications.waset.org/4024/nonlinear-time-history-analysis-of-3-dimensional-semi-rigid-steel-frames" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/4024/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/4024/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/4024/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/4024/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/4024/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/4024/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/4024/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/4024/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/4024/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/4024/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/4024.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">3954</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1046</span> Multigrid Bilateral Filter</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Zongqing%20Lu">Zongqing Lu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> It has proved that nonlinear diffusion and bilateral filtering (BF) have a closed connection. Early effort and contribution are to find a generalized representation to link them by using adaptive filtering. In this paper a new further relationship between nonlinear diffusion and bilateral filtering is explored which pays more attention to numerical calculus. We give a fresh idea that bilateral filtering can be accelerated by multigrid (MG) scheme which likes the nonlinear diffusion, and show that a bilateral filtering process with large kernel size can be approximated by a nonlinear diffusion process based on full multigrid (FMG) scheme. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Bilateral%20filter" title="Bilateral filter">Bilateral filter</a>, <a href="https://publications.waset.org/search?q=multigrid" title=" multigrid"> multigrid</a> </p> <a href="https://publications.waset.org/15927/multigrid-bilateral-filter" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/15927/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/15927/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/15927/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/15927/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/15927/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/15927/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/15927/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/15927/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/15927/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/15927/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/15927.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1863</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1045</span> Identification of Nonlinear Systems Using Radial Basis Function Neural Network</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=C.%20Pislaru">C. Pislaru</a>, <a href="https://publications.waset.org/search?q=A.%20Shebani"> A. Shebani</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>This paper uses the radial basis function neural network (RBFNN) for system identification of nonlinear systems. Five nonlinear systems are used to examine the activity of RBFNN in system modeling of nonlinear systems; the five nonlinear systems are dual tank system, single tank system, DC motor system, and two academic models. The feed forward method is considered in this work for modelling the non-linear dynamic models, where the KMeans clustering algorithm used in this paper to select the centers of radial basis function network, because it is reliable, offers fast convergence and can handle large data sets. The least mean square method is used to adjust the weights to the output layer, and Euclidean distance method used to measure the width of the Gaussian function.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=System%20identification" title="System identification">System identification</a>, <a href="https://publications.waset.org/search?q=Nonlinear%20system" title=" Nonlinear system"> Nonlinear system</a>, <a href="https://publications.waset.org/search?q=Neural%0D%0Anetworks" title=" Neural networks"> Neural networks</a>, <a href="https://publications.waset.org/search?q=RBF%20neural%20network." title=" RBF neural network."> RBF neural network.</a> </p> <a href="https://publications.waset.org/9999894/identification-of-nonlinear-systems-using-radial-basis-function-neural-network" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/9999894/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/9999894/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/9999894/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/9999894/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/9999894/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/9999894/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/9999894/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/9999894/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/9999894/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/9999894/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/9999894.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">2864</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1044</span> A New Verified Method for Solving Nonlinear Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Taher%20Lotfi">Taher Lotfi </a>, <a href="https://publications.waset.org/search?q=Parisa%20Bakhtiari"> Parisa Bakhtiari </a>, <a href="https://publications.waset.org/search?q=Katayoun%20Mahdiani"> Katayoun Mahdiani </a>, <a href="https://publications.waset.org/search?q=Mehdi%20Salimi"> Mehdi Salimi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper, verified extension of the Ostrowski method which calculates the enclosure solutions of a given nonlinear equation is introduced. Also, error analysis and convergence will be discussed. Some implemented examples with INTLAB are also included to illustrate the validity and applicability of the scheme.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Iinterval%20analysis" title="Iinterval analysis">Iinterval analysis</a>, <a href="https://publications.waset.org/search?q=nonlinear%20equations" title=" nonlinear equations"> nonlinear equations</a>, <a href="https://publications.waset.org/search?q=Ostrowski%0D%0Amethod." title=" Ostrowski method."> Ostrowski method.</a> </p> <a href="https://publications.waset.org/1886/a-new-verified-method-for-solving-nonlinear-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/1886/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/1886/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/1886/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/1886/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/1886/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/1886/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/1886/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/1886/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/1886/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/1886/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/1886.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1511</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1043</span> The Small Scale Effect on Nonlinear Vibration of Single Layer Graphene Sheets</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=E.%20Jomehzadeh">E. Jomehzadeh</a>, <a href="https://publications.waset.org/search?q=A.R.%20Saidi"> A.R. Saidi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In the present article, nonlinear vibration analysis of single layer graphene sheets is presented and the effect of small length scale is investigated. Using the Hamilton's principle, the three coupled nonlinear equations of motion are obtained based on the von Karman geometrical model and Eringen theory of nonlocal continuum. The solutions of Free nonlinear vibration, based on a one term mode shape, are found for both simply supported and clamped graphene sheets. A complete analysis of graphene sheets with movable as well as immovable in-plane conditions is also carried out. The results obtained herein are compared with those available in the literature for classical isotropic rectangular plates and excellent agreement is seen. Also, the nonlinear effects are presented as functions of geometric properties and small scale parameter. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Small%20scale" title="Small scale">Small scale</a>, <a href="https://publications.waset.org/search?q=Nonlinear%20vibration" title=" Nonlinear vibration"> Nonlinear vibration</a>, <a href="https://publications.waset.org/search?q=Graphene%20sheet" title=" Graphene sheet"> Graphene sheet</a>, <a href="https://publications.waset.org/search?q=Nonlocal%20continuum" title="Nonlocal continuum">Nonlocal continuum</a> </p> <a href="https://publications.waset.org/13486/the-small-scale-effect-on-nonlinear-vibration-of-single-layer-graphene-sheets" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/13486/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/13486/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/13486/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/13486/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/13486/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/13486/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/13486/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/13486/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/13486/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/13486/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/13486.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">2336</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1042</span> Effect of Implementation of Nonlinear Sequence Transformations on Power Series Expansion for a Class of Non-Linear Abel Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Javad%20Abdalkhani">Javad Abdalkhani</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Convergence of power series solutions for a class of non-linear Abel type equations, including an equation that arises in nonlinear cooling of semi-infinite rods, is very slow inside their small radius of convergence. Beyond that the corresponding power series are wildly divergent. Implementation of nonlinear sequence transformation allow effortless evaluation of these power series on very large intervals.. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Nonlinear%20transformation" title="Nonlinear transformation">Nonlinear transformation</a>, <a href="https://publications.waset.org/search?q=Abel%20Volterra%20Equations" title=" Abel Volterra Equations"> Abel Volterra Equations</a>, <a href="https://publications.waset.org/search?q=Mathematica" title="Mathematica">Mathematica</a> </p> <a href="https://publications.waset.org/1972/effect-of-implementation-of-nonlinear-sequence-transformations-on-power-series-expansion-for-a-class-of-non-linear-abel-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/1972/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/1972/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/1972/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/1972/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/1972/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/1972/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/1972/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/1972/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/1972/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/1972/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/1972.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1305</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1041</span> A Modification on Newton's Method for Solving Systems of Nonlinear Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Jafar%20Biazar">Jafar Biazar</a>, <a href="https://publications.waset.org/search?q=Behzad%20Ghanbari"> Behzad Ghanbari</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper, we are concerned with the further study for system of nonlinear equations. Since systems with inaccurate function values or problems with high computational cost arise frequently in science and engineering, recently such systems have attracted researcher-s interest. In this work we present a new method which is independent of function evolutions and has a quadratic convergence. This method can be viewed as a extension of some recent methods for solving mentioned systems of nonlinear equations. Numerical results of applying this method to some test problems show the efficiently and reliability of method.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=System%20of%20nonlinear%20equations." title="System of nonlinear equations.">System of nonlinear equations.</a> </p> <a href="https://publications.waset.org/13521/a-modification-on-newtons-method-for-solving-systems-of-nonlinear-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/13521/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/13521/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/13521/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/13521/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/13521/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/13521/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/13521/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/13521/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/13521/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/13521/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/13521.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1593</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1040</span> On the Approximate Solution of a Nonlinear Singular Integral Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Nizami%20Mustafa">Nizami Mustafa</a>, <a href="https://publications.waset.org/search?q=C.%20Ardil"> C. Ardil</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this study, the existence and uniqueness of the solution of a nonlinear singular integral equation that is defined on a region in the complex plane is proven and a method is given for finding the solution.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Approximate%20solution" title="Approximate solution">Approximate solution</a>, <a href="https://publications.waset.org/search?q=Fixed-point%20principle" title=" Fixed-point principle"> Fixed-point principle</a>, <a href="https://publications.waset.org/search?q=Nonlinear%20singular%20integral%20equations" title="Nonlinear singular integral equations">Nonlinear singular integral equations</a>, <a href="https://publications.waset.org/search?q=Vekua%20integral%20operator" title=" Vekua integral operator"> Vekua integral operator</a> </p> <a href="https://publications.waset.org/358/on-the-approximate-solution-of-a-nonlinear-singular-integral-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/358/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/358/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/358/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/358/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/358/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/358/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/358/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/358/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/358/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/358/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/358.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1923</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1039</span> Some Third Order Methods for Solving Systems of Nonlinear Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Janak%20Raj%20Sharma">Janak Raj Sharma</a>, <a href="https://publications.waset.org/search?q=Rajni%20Sharma"> Rajni Sharma</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Based on Traub-s methods for solving nonlinear equation f(x) = 0, we develop two families of third-order methods for solving system of nonlinear equations F(x) = 0. The families include well-known existing methods as special cases. The stability is corroborated by numerical results. Comparison with well-known methods shows that the present methods are robust. These higher order methods may be very useful in the numerical applications requiring high precision in their computations because these methods yield a clear reduction in number of iterations. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Nonlinear%20equations%20and%20systems" title="Nonlinear equations and systems">Nonlinear equations and systems</a>, <a href="https://publications.waset.org/search?q=Newton%27s%20method" title=" Newton's method"> Newton's method</a>, <a href="https://publications.waset.org/search?q=fixed%20point%20iteration" title=" fixed point iteration"> fixed point iteration</a>, <a href="https://publications.waset.org/search?q=order%20of%20convergence." title=" order of convergence."> order of convergence.</a> </p> <a href="https://publications.waset.org/1595/some-third-order-methods-for-solving-systems-of-nonlinear-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/1595/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/1595/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/1595/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/1595/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/1595/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/1595/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/1595/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/1595/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/1595/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/1595/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/1595.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">2207</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1038</span> State Estimation Method Based on Unscented Kalman Filter for Vehicle Nonlinear Dynamics</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Wataru%20Nakamura">Wataru Nakamura</a>, <a href="https://publications.waset.org/search?q=Tomoaki%20Hashimoto"> Tomoaki Hashimoto</a>, <a href="https://publications.waset.org/search?q=Liang-Kuang%20Chen"> Liang-Kuang Chen</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper provides a state estimation method for automatic control systems of nonlinear vehicle dynamics. A nonlinear tire model is employed to represent the realistic behavior of a vehicle. In general, all the state variables of control systems are not precisedly known, because those variables are observed through output sensors and limited parts of them might be only measurable. Hence, automatic control systems must incorporate some type of state estimation. It is needed to establish a state estimation method for nonlinear vehicle dynamics with restricted measurable state variables. For this purpose, unscented Kalman filter method is applied in this study for estimating the state variables of nonlinear vehicle dynamics. The objective of this paper is to propose a state estimation method using unscented Kalman filter for nonlinear vehicle dynamics. The effectiveness of the proposed method is verified by numerical simulations. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=State%20estimation" title="State estimation">State estimation</a>, <a href="https://publications.waset.org/search?q=control%20systems" title=" control systems"> control systems</a>, <a href="https://publications.waset.org/search?q=observer%20systems" title=" observer systems"> observer systems</a>, <a href="https://publications.waset.org/search?q=unscented%20Kalman%20filter" title=" unscented Kalman filter"> unscented Kalman filter</a>, <a href="https://publications.waset.org/search?q=nonlinear%20vehicle%20dynamics." title=" nonlinear vehicle dynamics."> nonlinear vehicle dynamics.</a> </p> <a href="https://publications.waset.org/10011696/state-estimation-method-based-on-unscented-kalman-filter-for-vehicle-nonlinear-dynamics" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10011696/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10011696/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10011696/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10011696/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10011696/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10011696/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10011696/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10011696/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10011696/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10011696/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10011696.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">613</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1037</span> Analytical Based Truncation Principle of Higher-Order Solution for a x1/3 Force Nonlinear Oscillator</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Md.%20Alal%20Hosen">Md. Alal Hosen</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper, a modified harmonic balance method based an analytical technique has been developed to determine higher-order approximate periodic solutions of a conservative nonlinear oscillator for which the elastic force term is proportional to x<sup>1/3</sup>. Usually, a set of nonlinear algebraic equations is solved in this method. However, analytical solutions of these algebraic equations are not always possible, especially in the case of a large oscillation. In this article, different parameters of the same nonlinear problems are found, for which the power series produces desired results even for the large oscillation. We find a modified harmonic balance method works very well for the whole range of initial amplitudes, and the excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. Besides these, a suitable truncation formula is found in which the solution measures better results than existing solutions. The method is mainly illustrated by the x<sup>1/3</sup> force nonlinear oscillator but it is also useful for many other nonlinear problems.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Approximate%20solutions" title="Approximate solutions">Approximate solutions</a>, <a href="https://publications.waset.org/search?q=Harmonic%20balance%20method" title=" Harmonic balance method"> Harmonic balance method</a>, <a href="https://publications.waset.org/search?q=Nonlinear%20oscillator" title=" Nonlinear oscillator"> Nonlinear oscillator</a>, <a href="https://publications.waset.org/search?q=Perturbation." title=" Perturbation. "> Perturbation. </a> </p> <a href="https://publications.waset.org/9996750/analytical-based-truncation-principle-of-higher-order-solution-for-a-x13-force-nonlinear-oscillator" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/9996750/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/9996750/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/9996750/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/9996750/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/9996750/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/9996750/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/9996750/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/9996750/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/9996750/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/9996750/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/9996750.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1431</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1036</span> Simulation of Propagation of Cos-Gaussian Beam in Strongly Nonlocal Nonlinear Media Using Paraxial Group Transformation </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=A.%20Keshavarz">A. Keshavarz</a>, <a href="https://publications.waset.org/search?q=Z.%20Roosta"> Z. Roosta</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper, propagation of cos-Gaussian beam in strongly nonlocal nonlinear media has been stimulated by using paraxial group transformation. At first, cos-Gaussian beam, nonlocal nonlinear media, critical power, transfer matrix, and paraxial group transformation are introduced. Then, the propagation of the cos-Gaussian beam in strongly nonlocal nonlinear media is simulated. Results show that beam propagation has periodic structure during self-focusing effect in this case. However, this simple method can be used for investigation of propagation of kinds of beams in ABCD optical media.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Paraxial%20group%20transformation" title="Paraxial group transformation">Paraxial group transformation</a>, <a href="https://publications.waset.org/search?q=nonlocal%20nonlinear%20media" title=" nonlocal nonlinear media"> nonlocal nonlinear media</a>, <a href="https://publications.waset.org/search?q=Cos-Gaussian%20beam" title=" Cos-Gaussian beam"> Cos-Gaussian beam</a>, <a href="https://publications.waset.org/search?q=ABCD%20law." title=" ABCD law."> ABCD law.</a> </p> <a href="https://publications.waset.org/10006913/simulation-of-propagation-of-cos-gaussian-beam-in-strongly-nonlocal-nonlinear-media-using-paraxial-group-transformation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10006913/apa" target="_blank" rel="nofollow" class="btn 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