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dynamical systems</title> <meta name="description" content="Search results for: hybrid dynamical systems"> <meta name="keywords" content="hybrid dynamical systems"> <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 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action="https://publications.waset.org/abstracts/search"> <div id="custom-search-input"> <div class="input-group"> <i class="fas fa-search"></i> <input type="text" class="search-query" name="q" placeholder="Author, Title, Abstract, Keywords" value="hybrid dynamical systems"> <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> 10847</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: hybrid dynamical systems</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10847</span> Dynamical Systems and Fibonacci Numbers</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Vandana%20N.%20Purav">Vandana N. Purav</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The Dynamical systems concept is a mathematical formalization for any fixed rule that describes the time dependence of a points position in its ambient space. e.g. pendulum of a clock, the number of fish each spring in a lake, the number of rabbits spring in an enclosure, etc. The Dynamical system theory used to describe the complex nature that is dynamical systems with differential equations called continuous dynamical system or dynamical system with difference equations called discrete dynamical system. The concept of dynamical system has its origin in Newtonian mechanics. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=dynamical%20systems" title="dynamical systems">dynamical systems</a>, <a href="https://publications.waset.org/abstracts/search?q=Fibonacci%20numbers" title=" Fibonacci numbers"> Fibonacci numbers</a>, <a href="https://publications.waset.org/abstracts/search?q=Newtonian%20mechanics" title=" Newtonian mechanics"> Newtonian mechanics</a>, <a href="https://publications.waset.org/abstracts/search?q=discrete%20dynamical%20system" title=" discrete dynamical system"> discrete dynamical system</a> </p> <a href="https://publications.waset.org/abstracts/25870/dynamical-systems-and-fibonacci-numbers" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/25870.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">492</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10846</span> Calculating Non-Unique Sliding Modes for Switched Dynamical Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Eugene%20Stepanov">Eugene Stepanov</a>, <a href="https://publications.waset.org/abstracts/search?q=Arkadi%20Ponossov"> Arkadi Ponossov</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Ordinary differential equations with switching nonlinearities constitute a very useful tool in many applications. The solutions of such equations can usually be calculated analytically if they cross the discontinuities transversally. Otherwise, one has trajectories that slides along the discontinuity, and the calculations become less straightforward in this case. For instance, one of the problems one faces is non-uniqueness of the sliding modes. In the presentation, it is proposed to apply the theory of hybrid dynamical systems to calculate the solutions that are ‘hidden’ in the discontinuities. Roughly, one equips the underlying switched system with an explicitly designed discrete dynamical system (‘automaton’), which governs the dynamics of the switched system. This construction ‘splits’ the dynamics, which, as it is shown in the presentation, gives uniqueness of the resulting hybrid trajectories and at the same time provides explicit formulae for them. Projecting the hybrid trajectories back onto the original continuous system explains non-uniqueness of its trajectories. The automaton is designed with the help of the attractors of the specially constructed adjoint dynamical system. Several examples are provided in the presentation, which supports the efficiency of the suggested scheme. The method can be of interest in control theory, gene regulatory networks, neural field models and other fields, where switched dynamics is a part of the analysis. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=hybrid%20dynamical%20systems" title="hybrid dynamical systems">hybrid dynamical systems</a>, <a href="https://publications.waset.org/abstracts/search?q=singular%20perturbation%20analysis" title=" singular perturbation analysis"> singular perturbation analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=sliding%20modes" title=" sliding modes"> sliding modes</a>, <a href="https://publications.waset.org/abstracts/search?q=switched%20dynamics" title=" switched dynamics"> switched dynamics</a> </p> <a href="https://publications.waset.org/abstracts/86304/calculating-non-unique-sliding-modes-for-switched-dynamical-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/86304.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">163</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10845</span> Projective Lag Synchronization in Drive-Response Dynamical Networks via Hybrid Feedback Control</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mohd%20Salmi%20Md%20Noorani">Mohd Salmi Md Noorani</a>, <a href="https://publications.waset.org/abstracts/search?q=Ghada%20Al-Mahbashi"> Ghada Al-Mahbashi</a>, <a href="https://publications.waset.org/abstracts/search?q=Sakhinah%20Abu%20Bakar"> Sakhinah Abu Bakar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper investigates projective lag synchronization (PLS) behavior in drive response dynamical networks (DRDNs) model with identical nodes. A hybrid feedback control method is designed to achieve the PLS with mismatch and without mismatch terms. The stability of the error dynamics is proven theoretically using the Lyapunov stability theory. Finally, analytical results show that the states of the dynamical network with non-delayed coupling can be asymptotically synchronized onto a desired scaling factor under the designed controller. Moreover, the numerical simulations results demonstrate the validity of the proposed method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=drive-response%20dynamical%20network" title="drive-response dynamical network">drive-response dynamical network</a>, <a href="https://publications.waset.org/abstracts/search?q=projective%20lag%20synchronization" title=" projective lag synchronization"> projective lag synchronization</a>, <a href="https://publications.waset.org/abstracts/search?q=hybrid%20feedback%20control" title=" hybrid feedback control"> hybrid feedback control</a>, <a href="https://publications.waset.org/abstracts/search?q=stability%20theory" title=" stability theory"> stability theory</a> </p> <a href="https://publications.waset.org/abstracts/14139/projective-lag-synchronization-in-drive-response-dynamical-networks-via-hybrid-feedback-control" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/14139.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">391</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10844</span> Solving Ill-Posed Initial Value Problems for Switched Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Eugene%20Stepanov">Eugene Stepanov</a>, <a href="https://publications.waset.org/abstracts/search?q=Arcady%20Ponosov"> Arcady Ponosov</a> </p> <p class="card-text"><strong>Abstract:</strong></p> To model gene regulatory networks one uses ordinary differential equations with switching nonlinearities, where the initial value problem is known to be well-posed if the trajectories cross the discontinuities transversally. Otherwise, the initial value problem is usually ill-posed, which lead to theoretical and numerical complications. In the presentation, it is proposed to apply the theory of hybrid dynamical systems, rather than switched ones, to regularize the problem. 'Hybridization' of the switched system means that one attaches a dynamic discrete component ('automaton'), which follows the trajectories of the original system and governs its dynamics at the points of ill-posedness of the initial value problem making it well-posed. The construction of the automaton is based on the classification of the attractors of the specially designed adjoint dynamical system. Several examples are provided in the presentation, which support the suggested analysis. The method can also be of interest in other applied fields, where differential equations contain switchings, e.g. in neural field models. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=hybrid%20dynamical%20systems" title="hybrid dynamical systems">hybrid dynamical systems</a>, <a href="https://publications.waset.org/abstracts/search?q=ill-posed%20problems" title=" ill-posed problems"> ill-posed problems</a>, <a href="https://publications.waset.org/abstracts/search?q=singular%20perturbation%20analysis" title=" singular perturbation analysis"> singular perturbation analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=switching%20nonlinearities" title=" switching nonlinearities"> switching nonlinearities</a> </p> <a href="https://publications.waset.org/abstracts/85884/solving-ill-posed-initial-value-problems-for-switched-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/85884.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">184</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10843</span> Model-Free Distributed Control of Dynamical Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Javad%20Khazaei">Javad Khazaei</a>, <a href="https://publications.waset.org/abstracts/search?q=Rick%20Blum"> Rick Blum</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Distributed control is an efficient and flexible approach for coordination of multi-agent systems. One of the main challenges in designing a distributed controller is identifying the governing dynamics of the dynamical systems. Data-driven system identification is currently undergoing a revolution. With the availability of high-fidelity measurements and historical data, model-free identification of dynamical systems can facilitate the control design without tedious modeling of high-dimensional and/or nonlinear systems. This paper develops a distributed control design using consensus theory for linear and nonlinear dynamical systems using sparse identification of system dynamics. Compared with existing consensus designs that heavily rely on knowing the detailed system dynamics, the proposed model-free design can accurately capture the dynamics of the system with available measurements and input data and provide guaranteed performance in consensus and tracking problems. Heterogeneous damped oscillators are chosen as examples of dynamical system for validation purposes. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=consensus%20tracking" title="consensus tracking">consensus tracking</a>, <a href="https://publications.waset.org/abstracts/search?q=distributed%20control" title=" distributed control"> distributed control</a>, <a href="https://publications.waset.org/abstracts/search?q=model-free%20control" title=" model-free control"> model-free control</a>, <a href="https://publications.waset.org/abstracts/search?q=sparse%20identification%20of%20dynamical%20systems" title=" sparse identification of dynamical systems"> sparse identification of dynamical systems</a> </p> <a href="https://publications.waset.org/abstracts/144452/model-free-distributed-control-of-dynamical-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/144452.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">266</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10842</span> On the Solution of Fractional-Order Dynamical Systems Endowed with Block Hybrid Methods</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Kizito%20Ugochukwu%20Nwajeri">Kizito Ugochukwu Nwajeri</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper presents a distinct approach to solving fractional dynamical systems using hybrid block methods (HBMs). Fractional calculus extends the concept of derivatives and integrals to non-integer orders and finds increasing application in fields such as physics, engineering, and finance. However, traditional numerical techniques often struggle to accurately capture the complex behaviors exhibited by these systems. To address this challenge, we develop HBMs that integrate single-step and multi-step methods, enabling the simultaneous computation of multiple solution points while maintaining high accuracy. Our approach employs polynomial interpolation and collocation techniques to derive a system of equations that effectively models the dynamics of fractional systems. We also directly incorporate boundary and initial conditions into the formulation, enhancing the stability and convergence properties of the numerical solution. An adaptive step-size mechanism is introduced to optimize performance based on the local behavior of the solution. Extensive numerical simulations are conducted to evaluate the proposed methods, demonstrating significant improvements in accuracy and efficiency compared to traditional numerical approaches. The results indicate that our hybrid block methods are robust and versatile, making them suitable for a wide range of applications involving fractional dynamical systems. This work contributes to the existing literature by providing an effective numerical framework for analyzing complex behaviors in fractional systems, thereby opening new avenues for research and practical implementation across various disciplines. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fractional%20calculus" title="fractional calculus">fractional calculus</a>, <a href="https://publications.waset.org/abstracts/search?q=numerical%20simulation" title=" numerical simulation"> numerical simulation</a>, <a href="https://publications.waset.org/abstracts/search?q=stability%20and%20convergence" title=" stability and convergence"> stability and convergence</a>, <a href="https://publications.waset.org/abstracts/search?q=Adaptive%20step-size%20mechanism" title=" Adaptive step-size mechanism"> Adaptive step-size mechanism</a>, <a href="https://publications.waset.org/abstracts/search?q=collocation%20methods" title=" collocation methods"> collocation methods</a> </p> <a href="https://publications.waset.org/abstracts/188911/on-the-solution-of-fractional-order-dynamical-systems-endowed-with-block-hybrid-methods" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/188911.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">44</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10841</span> On the Topological Entropy of Nonlinear Dynamical Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Graziano%20Chesi">Graziano Chesi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The topological entropy plays a key role in linear dynamical systems, allowing one to establish the existence of stabilizing feedback controllers for linear systems in the presence of communications constraints. This paper addresses the determination of a robust value of the topological entropy in nonlinear dynamical systems, specifically the largest value of the topological entropy over all linearized models in a region of interest of the state space. It is shown that a sufficient condition for establishing upper bounds of the sought robust value of the topological entropy can be given in terms of a semidefinite program (SDP), which belongs to the class of convex optimization problems. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=non-linear%20system" title="non-linear system">non-linear system</a>, <a href="https://publications.waset.org/abstracts/search?q=communication%20constraint" title=" communication constraint"> communication constraint</a>, <a href="https://publications.waset.org/abstracts/search?q=topological%20entropy" title=" topological entropy"> topological entropy</a> </p> <a href="https://publications.waset.org/abstracts/45742/on-the-topological-entropy-of-nonlinear-dynamical-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/45742.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">323</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10840</span> Parameter Estimation in Dynamical Systems Based on Latent Variables</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Arcady%20Ponosov">Arcady Ponosov</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A novel mathematical approach is suggested, which facilitates a compressed representation and efficient validation of parameter-rich ordinary differential equation models describing the dynamics of complex, especially biology-related, systems and which is based on identification of the system's latent variables. In particular, an efficient parameter estimation method for the compressed non-linear dynamical systems is developed. The method is applied to the so-called 'power-law systems' being non-linear differential equations typically used in Biochemical System Theory. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=generalized%20law%20of%20mass%20action" title="generalized law of mass action">generalized law of mass action</a>, <a href="https://publications.waset.org/abstracts/search?q=metamodels" title=" metamodels"> metamodels</a>, <a href="https://publications.waset.org/abstracts/search?q=principal%20components" title=" principal components"> principal components</a>, <a href="https://publications.waset.org/abstracts/search?q=synergetic%20systems" title=" synergetic systems"> synergetic systems</a> </p> <a href="https://publications.waset.org/abstracts/42041/parameter-estimation-in-dynamical-systems-based-on-latent-variables" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/42041.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">355</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10839</span> A Dynamical Approach for Relating Energy Consumption to Hybrid Inventory Level in the Supply Chain</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Benga%20Ebouele">Benga Ebouele</a>, <a href="https://publications.waset.org/abstracts/search?q=Thomas%20Tengen"> Thomas Tengen</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Due to long lead time, work in process (WIP) inventory can manifest within the supply chain of most manufacturing system. It implies that there are lesser finished good on hand and more in the process because the work remains in the factory too long and cannot be sold to either customers The supply chain of most manufacturing system is then considered as inefficient as it take so much time to produce the finished good. Time consumed in each operation of the supply chain has an associated energy costs. Such phenomena can be harmful for a hybrid inventory system because a lot of space to store these semi-finished goods may be needed and one is not sure about the final energy cost of producing, holding and delivering the good to customers. The principle that reduces waste of energy within the supply chain of most manufacturing firms should therefore be available to all inventory managers in pursuit of profitability. Decision making by inventory managers in this condition is a modeling process, whereby a dynamical approach is used to depict, examine, specify and even operationalize the relationship between energy consumption and hybrid inventory level. The relationship between energy consumption and inventory level is established, which indicates a poor level of control and hence a potential for energy savings. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=dynamic%20modelling" title="dynamic modelling">dynamic modelling</a>, <a href="https://publications.waset.org/abstracts/search?q=energy%20used" title=" energy used"> energy used</a>, <a href="https://publications.waset.org/abstracts/search?q=hybrid%20inventory" title=" hybrid inventory"> hybrid inventory</a>, <a href="https://publications.waset.org/abstracts/search?q=supply%20chain" title=" supply chain"> supply chain</a> </p> <a href="https://publications.waset.org/abstracts/41799/a-dynamical-approach-for-relating-energy-consumption-to-hybrid-inventory-level-in-the-supply-chain" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/41799.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">268</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10838</span> A Hybrid Method for Determination of Effective Poles Using Clustering Dominant Pole Algorithm </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Anuj%20Abraham">Anuj Abraham</a>, <a href="https://publications.waset.org/abstracts/search?q=N.%20Pappa"> N. Pappa</a>, <a href="https://publications.waset.org/abstracts/search?q=Daniel%20Honc"> Daniel Honc</a>, <a href="https://publications.waset.org/abstracts/search?q=Rahul%20Sharma"> Rahul Sharma</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, an analysis of some model order reduction techniques is presented. A new hybrid algorithm for model order reduction of linear time invariant systems is compared with the conventional techniques namely Balanced Truncation, Hankel Norm reduction and Dominant Pole Algorithm (DPA). The proposed hybrid algorithm is known as Clustering Dominant Pole Algorithm (CDPA) is able to compute the full set of dominant poles and its cluster center efficiently. The dominant poles of a transfer function are specific eigenvalues of the state space matrix of the corresponding dynamical system. The effectiveness of this novel technique is shown through the simulation results. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=balanced%20truncation" title="balanced truncation">balanced truncation</a>, <a href="https://publications.waset.org/abstracts/search?q=clustering" title=" clustering"> clustering</a>, <a href="https://publications.waset.org/abstracts/search?q=dominant%20pole" title=" dominant pole"> dominant pole</a>, <a href="https://publications.waset.org/abstracts/search?q=Hankel%20norm" title=" Hankel norm"> Hankel norm</a>, <a href="https://publications.waset.org/abstracts/search?q=model%20reduction" title=" model reduction"> model reduction</a> </p> <a href="https://publications.waset.org/abstracts/17480/a-hybrid-method-for-determination-of-effective-poles-using-clustering-dominant-pole-algorithm" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/17480.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">599</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10837</span> Overview of Different Approaches Used in Optimal Operation Control of Hybrid Renewable Energy Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=K.%20Kusakana">K. Kusakana </a> </p> <p class="card-text"><strong>Abstract:</strong></p> A hybrid energy system is a combination of renewable energy sources with back up, as well as a storage system used to respond to given load energy requirements. Given that the electrical output of each renewable source is fluctuating with changes in weather conditions, and since the load demand also varies with time; one of the main attributes of hybrid systems is to be able to respond to the load demand at any time by optimally controlling each energy source, storage and back-up system. The induced optimization problem is to compute the optimal operation control of the system with the aim of minimizing operation costs while efficiently and reliably responding to the load energy requirement. Current optimization research and development on hybrid systems are mainly focusing on the sizing aspect. Thus, the aim of this paper is to report on the state-of-the-art of optimal operation control of hybrid renewable energy systems. This paper also discusses different challenges encountered, as well as future developments that can help in improving the optimal operation control of hybrid renewable energy systems. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=renewable%20energies" title="renewable energies">renewable energies</a>, <a href="https://publications.waset.org/abstracts/search?q=hybrid%20systems" title=" hybrid systems"> hybrid systems</a>, <a href="https://publications.waset.org/abstracts/search?q=optimization" title=" optimization"> optimization</a>, <a href="https://publications.waset.org/abstracts/search?q=operation%20control" title=" operation control"> operation control</a> </p> <a href="https://publications.waset.org/abstracts/48787/overview-of-different-approaches-used-in-optimal-operation-control-of-hybrid-renewable-energy-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/48787.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">379</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10836</span> Efficient Neural and Fuzzy Models for the Identification of Dynamical Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Aouiche%20Abdelaziz">Aouiche Abdelaziz</a>, <a href="https://publications.waset.org/abstracts/search?q=Soudani%20Mouhamed%20Salah"> Soudani Mouhamed Salah</a>, <a href="https://publications.waset.org/abstracts/search?q=Aouiche%20El%20Moundhe"> Aouiche El Moundhe</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The present paper addresses the utilization of Artificial Neural Networks (ANNs) and Fuzzy Inference Systems (FISs) for the identification and control of dynamical systems with some degree of uncertainty. Because ANNs and FISs have an inherent ability to approximate functions and to adapt to changes in input and parameters, they can be used to control systems too complex for linear controllers. In this work, we show how ANNs and FISs can be put in order to form nets that can learn from external data. In sequence, it is presented structures of inputs that can be used along with ANNs and FISs to model non-linear systems. Four systems were used to test the identification and control of the structures proposed. The results show the ANNs and FISs (Back Propagation Algorithm) used were efficient in modeling and controlling the non-linear plants. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=non-linear%20systems" title="non-linear systems">non-linear systems</a>, <a href="https://publications.waset.org/abstracts/search?q=fuzzy%20set%20Models" title=" fuzzy set Models"> fuzzy set Models</a>, <a href="https://publications.waset.org/abstracts/search?q=neural%20network" title=" neural network"> neural network</a>, <a href="https://publications.waset.org/abstracts/search?q=control%20law" title=" control law"> control law</a> </p> <a href="https://publications.waset.org/abstracts/142525/efficient-neural-and-fuzzy-models-for-the-identification-of-dynamical-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/142525.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">212</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10835</span> Numerical Regularization of Ill-Posed Problems via Hybrid Feedback Controls</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Eugene%20Stepanov">Eugene Stepanov</a>, <a href="https://publications.waset.org/abstracts/search?q=Arkadi%20Ponossov"> Arkadi Ponossov</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Many mathematical models used in biological and other applications are ill-posed. The reason for that is the nature of differential equations, where the nonlinearities are assumed to be step functions, which is done to simplify the analysis. Prominent examples are switched systems arising from gene regulatory networks and neural field equations. This simplification leads, however, to theoretical and numerical complications. In the presentation, it is proposed to apply the theory of hybrid feedback controls to regularize the problem. Roughly speaking, one attaches a finite state control (‘automaton’), which follows the trajectories of the original system and governs its dynamics at the points of ill-posedness. The construction of the automaton is based on the classification of the attractors of the specially designed adjoint dynamical system. This ‘hybridization’ is shown to regularize the original switched system and gives rise to efficient hybrid numerical schemes. Several examples are provided in the presentation, which supports the suggested analysis. The method can be of interest in other applied fields, where differential equations contain step-like nonlinearities. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=hybrid%20feedback%20control" title="hybrid feedback control">hybrid feedback control</a>, <a href="https://publications.waset.org/abstracts/search?q=ill-posed%20problems" title=" ill-posed problems"> ill-posed problems</a>, <a href="https://publications.waset.org/abstracts/search?q=singular%20perturbation%20analysis" title=" singular perturbation analysis"> singular perturbation analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=step-like%20nonlinearities" title=" step-like nonlinearities"> step-like nonlinearities</a> </p> <a href="https://publications.waset.org/abstracts/86303/numerical-regularization-of-ill-posed-problems-via-hybrid-feedback-controls" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/86303.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">245</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10834</span> Fractal Analysis of Some Bifurcations of Discrete Dynamical Systems in Higher Dimensions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Lana%20Horvat%20Dmitrovi%C4%87">Lana Horvat Dmitrović</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The main purpose of this paper is to study the box dimension as fractal property of bifurcations of discrete dynamical systems in higher dimensions. The paper contains the fractal analysis of the orbits near the hyperbolic and non-hyperbolic fixed points in discrete dynamical systems. It is already known that in one-dimensional case the orbit near the hyperbolic fixed point has the box dimension equal to zero. On the other hand, the orbit near the non-hyperbolic fixed point has strictly positive box dimension which is connected to the non-degeneracy condition of certain bifurcation. One of the main results in this paper is the generalisation of results about box dimension near the hyperbolic and non-hyperbolic fixed points to higher dimensions. In the process of determining box dimension, the restriction of systems to stable, unstable and center manifolds, Lipschitz property of box dimension and the notion of projective box dimension are used. The analysis of the bifurcations in higher dimensions with one multiplier on the unit circle is done by using the normal forms on one-dimensional center manifolds. This specific change in box dimension of an orbit at the moment of bifurcation has already been explored for some bifurcations in one and two dimensions. It was shown that specific values of box dimension are connected to appropriate bifurcations such as fold, flip, cusp or Neimark-Sacker bifurcation. This paper further explores this connection of box dimension as fractal property to some specific bifurcations in higher dimensions, such as fold-flip and flip-Neimark-Sacker. Furthermore, the application of the results to the unit time map of continuous dynamical system near hyperbolic and non-hyperbolic singularities is presented. In that way, box dimensions which are specific for certain bifurcations of continuous systems can be obtained. The approach to bifurcation analysis by using the box dimension as specific fractal property of orbits can lead to better understanding of bifurcation phenomenon. It could also be useful in detecting the existence or nonexistence of bifurcations of discrete and continuous dynamical systems. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=bifurcation" title="bifurcation">bifurcation</a>, <a href="https://publications.waset.org/abstracts/search?q=box%20dimension" title=" box dimension"> box dimension</a>, <a href="https://publications.waset.org/abstracts/search?q=invariant%20manifold" title=" invariant manifold"> invariant manifold</a>, <a href="https://publications.waset.org/abstracts/search?q=orbit%20near%20fixed%20point" title=" orbit near fixed point"> orbit near fixed point</a> </p> <a href="https://publications.waset.org/abstracts/52891/fractal-analysis-of-some-bifurcations-of-discrete-dynamical-systems-in-higher-dimensions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/52891.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">254</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10833</span> Network Connectivity Knowledge Graph Using Dwave Quantum Hybrid Solvers</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Nivedha%20Rajaram">Nivedha Rajaram</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Hybrid Quantum solvers have been given prime focus in recent days by computation problem-solving domain industrial applications. D’Wave Quantum Computers are one such paragon of systems built using quantum annealing mechanism. Discrete Quadratic Models is a hybrid quantum computing model class supplied by D’Wave Ocean SDK - a real-time software platform for hybrid quantum solvers. These hybrid quantum computing modellers can be employed to solve classic problems. One such problem that we consider in this paper is finding a network connectivity knowledge hub in a huge network of systems. Using this quantum solver, we try to find out the prime system hub, which acts as a supreme connection point for the set of connected computers in a large network. This paper establishes an innovative problem approach to generate a connectivity system hub plot for a set of systems using DWave ocean SDK hybrid quantum solvers. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=quantum%20computing" title="quantum computing">quantum computing</a>, <a href="https://publications.waset.org/abstracts/search?q=hybrid%20quantum%20solver" title=" hybrid quantum solver"> hybrid quantum solver</a>, <a href="https://publications.waset.org/abstracts/search?q=DWave%20annealing" title=" DWave annealing"> DWave annealing</a>, <a href="https://publications.waset.org/abstracts/search?q=network%20knowledge%20graph" title=" network knowledge graph"> network knowledge graph</a> </p> <a href="https://publications.waset.org/abstracts/150932/network-connectivity-knowledge-graph-using-dwave-quantum-hybrid-solvers" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/150932.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">127</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10832</span> Modeling and Controlling Nonlinear Dynamical Effects in Non-Contact Superconducting and Diamagnetic Suspensions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sergey%20Kuznetsov">Sergey Kuznetsov</a>, <a href="https://publications.waset.org/abstracts/search?q=Yuri%20Urman"> Yuri Urman</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We present an approach to investigate non-linear dynamical effects occurring in the noncontact superconducting and diamagnetic suspensions, when levitated body has finite size. This approach is based on the calculation of interaction energy between spherical finite size superconducting or diamagnetic body with external magnetic field. Effects of small deviations from spherical shape may be also taken into account by introducing small corrections to the energy. This model allows investigating dynamical effects important for practical applications, such as nonlinear resonances, change of vibration plane, coupling of rotational and translational motions etc. We also show how the geometry of suspension affects various dynamical effects and how an inverse problem may be formulated to enforce or diminish various dynamical effects. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=levitation" title="levitation">levitation</a>, <a href="https://publications.waset.org/abstracts/search?q=non-linear%20dynamics" title=" non-linear dynamics"> non-linear dynamics</a>, <a href="https://publications.waset.org/abstracts/search?q=superconducting" title=" superconducting"> superconducting</a>, <a href="https://publications.waset.org/abstracts/search?q=diamagnetic%20stability" title=" diamagnetic stability "> diamagnetic stability </a> </p> <a href="https://publications.waset.org/abstracts/47249/modeling-and-controlling-nonlinear-dynamical-effects-in-non-contact-superconducting-and-diamagnetic-suspensions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/47249.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">410</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10831</span> Distributed Energy System - Microgrid Integration of Hybrid Power Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Pedro%20Esteban">Pedro Esteban</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Planning a hybrid power system (HPS) that integrates renewable generation sources, non-renewable generation sources and energy storage, involves determining the capacity and size of various components to be used in the system to be able to supply reliable electricity to the connected load as required. Nowadays it is very common to integrate solar photovoltaic (PV) power plants for renewable generation as part of HPS. The solar PV system is usually balanced via a second form of generation (renewable such as wind power or using fossil fuels such as a diesel generator) or an energy storage system (such as a battery bank). Hybrid power systems can also provide other forms of power such as heat for some applications. Modern hybrid power systems combine power generation and energy storage technologies together with real-time energy management and innovative power quality and energy efficiency improvement functionalities. These systems help customers achieve targets for clean energy generation, they add flexibility to the electrical grid, and they optimize the installation by improving its power quality and energy efficiency. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=microgrids" title="microgrids">microgrids</a>, <a href="https://publications.waset.org/abstracts/search?q=hybrid%20power%20systems" title=" hybrid power systems"> hybrid power systems</a>, <a href="https://publications.waset.org/abstracts/search?q=energy%20storage" title=" energy storage"> energy storage</a>, <a href="https://publications.waset.org/abstracts/search?q=grid%20code%20compliance" title=" grid code compliance"> grid code compliance</a> </p> <a href="https://publications.waset.org/abstracts/127226/distributed-energy-system-microgrid-integration-of-hybrid-power-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/127226.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">146</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10830</span> An Inverse Optimal Control Approach for the Nonlinear System Design Using ANN</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=M.%20P.%20Nanda%20Kumar">M. P. Nanda Kumar</a>, <a href="https://publications.waset.org/abstracts/search?q=K.%20Dheeraj"> K. Dheeraj</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The design of a feedback controller, so as to minimize a given performance criterion, for a general non-linear dynamical system is difficult; if not impossible. But for a large class of non-linear dynamical systems, the open loop control that minimizes a performance criterion can be obtained using calculus of variations and Pontryagin’s minimum principle. In this paper, the open loop optimal trajectories, that minimizes a given performance measure, is used to train the neural network whose inputs are state variables of non-linear dynamical systems and the open loop optimal control as the desired output. This trained neural network is used as the feedback controller. In other words, attempts are made here to solve the “inverse optimal control problem” by using the state and control trajectories that are optimal in an open loop sense. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=inverse%20optimal%20control" title="inverse optimal control">inverse optimal control</a>, <a href="https://publications.waset.org/abstracts/search?q=radial%20basis%20function" title=" radial basis function"> radial basis function</a>, <a href="https://publications.waset.org/abstracts/search?q=neural%20network" title=" neural network"> neural network</a>, <a href="https://publications.waset.org/abstracts/search?q=controller%20design" title=" controller design"> controller design</a> </p> <a href="https://publications.waset.org/abstracts/9888/an-inverse-optimal-control-approach-for-the-nonlinear-system-design-using-ann" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/9888.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">554</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10829</span> Time-Evolving Wave Packet in Phase Space</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mitsuyoshi%20Tomiya">Mitsuyoshi Tomiya</a>, <a href="https://publications.waset.org/abstracts/search?q=Kentaro%20Kawamura"> Kentaro Kawamura</a>, <a href="https://publications.waset.org/abstracts/search?q=Shoichi%20Sakamoto"> Shoichi Sakamoto</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In chaotic billiard systems, scar-like localization has been found on time-evolving wave packet. We may call it the “dynamical scar” to separate it to the original scar in stationary states. It also comes out along the vicinity of classical unstable periodic orbits, when the wave packets are launched along the orbits, against the hypothesis that the waves become homogenous all around the billiard. Then time-evolving wave packets are investigated numerically in phase space. The Wigner function is adopted to detect the wave packets in phase space. The 2-dimensional Poincaré sections of the 4-dimensional phase space are introduced to clarify the dynamical behavior of the wave packets. The Poincaré sections of the coordinate (x or y) and the momentum (Px or Py) can visualize the dynamical behavior of the wave packets, including the behavior in the momentum degree also. For example, in “dynamical scar” states, a bit larger momentum component comes first, and then the a bit smaller and smaller components follow next. The sections made in the momentum space (Px or Py) elucidates specific trajectories that have larger contribution to the “dynamical scar” states. It is the fixed point observation of the momentum degrees at a specific fixed point(x0, y0) in the phase space. The accumulation are also calculated to search the “dynamical scar” in the Poincare sections. It is found the scars as bright spots in momentum degrees of the phase space. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=chaotic%20billiard" title="chaotic billiard">chaotic billiard</a>, <a href="https://publications.waset.org/abstracts/search?q=Poincar%C3%A9%20section" title=" Poincaré section"> Poincaré section</a>, <a href="https://publications.waset.org/abstracts/search?q=scar" title=" scar"> scar</a>, <a href="https://publications.waset.org/abstracts/search?q=wave%20packet" title=" wave packet"> wave packet</a> </p> <a href="https://publications.waset.org/abstracts/32869/time-evolving-wave-packet-in-phase-space" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/32869.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">452</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10828</span> A Combined Error Control with Forward Euler Method for Dynamical Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=R.%20Vigneswaran">R. Vigneswaran</a>, <a href="https://publications.waset.org/abstracts/search?q=S.%20Thilakanathan"> S. Thilakanathan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Variable time-stepping algorithms for solving dynamical systems performed poorly for long time computations which pass close to a fixed point. To overcome this difficulty, several authors considered phase space error controls for numerical simulation of dynamical systems. In one generalized phase space error control, a step-size selection scheme was proposed, which allows this error control to be incorporated into the standard adaptive algorithm as an extra constraint at negligible extra computational cost. For this generalized error control, it was already analyzed the forward Euler method applied to the linear system whose coefficient matrix has real and negative eigenvalues. In this paper, this result was extended to the linear system whose coefficient matrix has complex eigenvalues with negative real parts. Some theoretical results were obtained and numerical experiments were carried out to support the theoretical results. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=adaptivity" title="adaptivity">adaptivity</a>, <a href="https://publications.waset.org/abstracts/search?q=fixed%20point" title=" fixed point"> fixed point</a>, <a href="https://publications.waset.org/abstracts/search?q=long%20time%20simulations" title=" long time simulations"> long time simulations</a>, <a href="https://publications.waset.org/abstracts/search?q=stability" title=" stability"> stability</a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20system" title=" linear system"> linear system</a> </p> <a href="https://publications.waset.org/abstracts/48246/a-combined-error-control-with-forward-euler-method-for-dynamical-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/48246.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">312</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10827</span> H∞ Takagi-Sugeno Fuzzy State-Derivative Feedback Control Design for Nonlinear Dynamic Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=N.%20Kaewpraek">N. Kaewpraek</a>, <a href="https://publications.waset.org/abstracts/search?q=W.%20Assawinchaichote"> W. Assawinchaichote </a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper considers an <em>H</em><sub>∞</sub> TS fuzzy state-derivative feedback controller for a class of nonlinear dynamical systems. A Takagi-Sugeno (TS) fuzzy model is used to approximate a class of nonlinear dynamical systems. Then, based on a linear matrix inequality (LMI) approach, we design an <em>H</em><sub>∞ </sub>TS fuzzy state-derivative feedback control law which guarantees <em>L</em><sub>2</sub>-gain of the mapping from the exogenous input noise to the regulated output to be less or equal to a prescribed value. We derive a sufficient condition such that the system with the fuzzy controller is asymptotically stable and <em>H</em><sub>∞</sub> performance is satisfied. Finally, we provide and simulate a numerical example is provided to illustrate the stability and the effectiveness of the proposed controller. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=h-infinity%20fuzzy%20control" title="h-infinity fuzzy control">h-infinity fuzzy control</a>, <a href="https://publications.waset.org/abstracts/search?q=an%20LMI%20approach" title=" an LMI approach"> an LMI approach</a>, <a href="https://publications.waset.org/abstracts/search?q=Takagi-Sugano%20%28TS%29%20fuzzy%20system" title=" Takagi-Sugano (TS) fuzzy system"> Takagi-Sugano (TS) fuzzy system</a>, <a href="https://publications.waset.org/abstracts/search?q=the%20photovoltaic%20systems" title=" the photovoltaic systems"> the photovoltaic systems</a> </p> <a href="https://publications.waset.org/abstracts/37998/h-takagi-sugeno-fuzzy-state-derivative-feedback-control-design-for-nonlinear-dynamic-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/37998.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">384</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10826</span> A Nonlinear Dynamical System with Application</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Abdullah%20Eqal%20Al%20Mazrooei">Abdullah Eqal Al Mazrooei</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, a nonlinear dynamical system is presented. This system is a bilinear class. The bilinear systems are very important kind of nonlinear systems because they have many applications in real life. They are used in biology, chemistry, manufacturing, engineering, and economics where linear models are ineffective or inadequate. They have also been recently used to analyze and forecast weather conditions. Bilinear systems have three advantages: First, they define many problems which have a great applied importance. Second, they give us approximations to nonlinear systems. Thirdly, they have a rich geometric and algebraic structures, which promises to be a fruitful field of research for scientists and applications. The type of nonlinearity that is treated and analyzed consists of bilinear interaction between the states vectors and the system input. By using some properties of the tensor product, these systems can be transformed to linear systems. But, here we discuss the nonlinearity when the state vector is multiplied by itself. So, this model will be able to handle evolutions according to the Lotka-Volterra models or the Lorenz weather models, thus enabling a wider and more flexible application of such models. Here we apply by using an estimator to estimate temperatures. The results prove the efficiency of the proposed system. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Lorenz%20models" title="Lorenz models">Lorenz models</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20systems" title=" nonlinear systems"> nonlinear systems</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20estimator" title=" nonlinear estimator"> nonlinear estimator</a>, <a href="https://publications.waset.org/abstracts/search?q=state-space%20model" title=" state-space model"> state-space model</a> </p> <a href="https://publications.waset.org/abstracts/60388/a-nonlinear-dynamical-system-with-application" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/60388.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">254</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10825</span> Trimma: Trimming Metadata Storage and Latency for Hybrid Memory Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Yiwei%20Li">Yiwei Li</a>, <a href="https://publications.waset.org/abstracts/search?q=Boyu%20Tian"> Boyu Tian</a>, <a href="https://publications.waset.org/abstracts/search?q=Mingyu%20Gao"> Mingyu Gao</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Hybrid main memory systems combine both performance and capacity advantages from heterogeneous memory technologies. With larger capacities, higher associativities, and finer granularities, hybrid memory systems currently exhibit significant metadata storage and lookup overheads for flexibly remapping data blocks between the two memory tiers. To alleviate the inefficiencies of existing designs, we propose Trimma, the combination of a multi-level metadata structure and an efficient metadata cache design. Trimma uses a multilevel metadata table to only track truly necessary address remap entries. The saved memory space is effectively utilized as extra DRAM cache capacity to improve performance. Trimma also uses separate formats to store the entries with non-identity and identity mappings. This improves the overall remap cache hit rate, further boosting the performance. Trimma is transparent to software and compatible with various types of hybrid memory systems. When evaluated on a representative DDR4 + NVM hybrid memory system, Trimma achieves up to 2.4× and on average 58.1% speedup benefits, compared with a state-of-the-art design that only leverages the unallocated fast memory space for caching. Trimma addresses metadata management overheads and targets future scalable large-scale hybrid memory architectures. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=memory%20system" title="memory system">memory system</a>, <a href="https://publications.waset.org/abstracts/search?q=data%20cache" title=" data cache"> data cache</a>, <a href="https://publications.waset.org/abstracts/search?q=hybrid%20memory" title=" hybrid memory"> hybrid memory</a>, <a href="https://publications.waset.org/abstracts/search?q=non-volatile%20memory" title=" non-volatile memory"> non-volatile memory</a> </p> <a href="https://publications.waset.org/abstracts/183183/trimma-trimming-metadata-storage-and-latency-for-hybrid-memory-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/183183.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">79</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10824</span> Hybrid Diagrid System for High-Rise Buildings</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Seyed%20Saeid%20Tabaee">Seyed Saeid Tabaee</a>, <a href="https://publications.waset.org/abstracts/search?q=Mohammad%20Afshari"> Mohammad Afshari</a>, <a href="https://publications.waset.org/abstracts/search?q=Bahador%20Ziaeemehr"> Bahador Ziaeemehr</a>, <a href="https://publications.waset.org/abstracts/search?q=Omid%20Bahar"> Omid Bahar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Nowadays, using modern structural systems with specific capabilities, like Diagrid, is emerging around the world. In this paper, a new resisting system, a combination of both Diagrid axial behavior and proper seismic performance of regular moment frames in tall buildings, named 'Hybrid Diagrid' is presented. The scaled specimen of the suggested hybrid system was built and tested using IIEES shaking table. The natural frequency and structural response of the analytical model were updated with the real experimental results. In order to compare its performance with the traditional Diagrid and moment frame systems, time history analysis was carried out. Extensive analysis shows the efficient seismic responses and economical behavior of Hybrid Diagrid structure with respect to the other two systems. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=hybrid%20diagrid%20system" title="hybrid diagrid system">hybrid diagrid system</a>, <a href="https://publications.waset.org/abstracts/search?q=moment%20frame" title=" moment frame"> moment frame</a>, <a href="https://publications.waset.org/abstracts/search?q=shaking%20table" title=" shaking table"> shaking table</a>, <a href="https://publications.waset.org/abstracts/search?q=tall%20buildings" title=" tall buildings"> tall buildings</a>, <a href="https://publications.waset.org/abstracts/search?q=time%20history%20analysis" title=" time history analysis"> time history analysis</a> </p> <a href="https://publications.waset.org/abstracts/83299/hybrid-diagrid-system-for-high-rise-buildings" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/83299.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">215</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10823</span> Reconstruction and Rejection of External Disturbances in a Dynamical System</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Iftikhar%20Ahmad">Iftikhar Ahmad</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20Benallegue"> A. Benallegue</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20El%20Hadri"> A. El Hadri</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we have proposed an observer for the reconstruction and a control law for the rejection application of unknown bounded external disturbance in a dynamical system. The strategy of both the observer and the controller is designed like a second order sliding mode with a proportional-integral (PI) term. Lyapunov theory is used to prove the exponential convergence and stability. Simulations results are given to show the performance of this method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=non-linear%20systems" title="non-linear systems">non-linear systems</a>, <a href="https://publications.waset.org/abstracts/search?q=sliding%20mode%20observer" title=" sliding mode observer"> sliding mode observer</a>, <a href="https://publications.waset.org/abstracts/search?q=disturbance%20rejection" title=" disturbance rejection"> disturbance rejection</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20control" title=" nonlinear control"> nonlinear control</a> </p> <a href="https://publications.waset.org/abstracts/44910/reconstruction-and-rejection-of-external-disturbances-in-a-dynamical-system" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/44910.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">334</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10822</span> Chaos Analysis of a 3D Finance System and Generalized Synchronization for N-Dimension</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Muhammad%20Fiaz">Muhammad Fiaz</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The article in hand is the study of complex features like Zero Hopf Bifurcation, Chaos and Synchronization of integer and fractional order version of a new 3D finance system. Trusted tools of averaging theory and active control method are utilized for investigation of Zero Hopf bifurcation and synchronization for both versions respectively. Inventiveness of the paper is to find the answer of a question that is it possible to find a chaotic system which can be synchronized with any other of the same dimension? Based on different examples we categorically develop a theory that if a couple of master and slave chaotic dynamical system is synchronized by selecting a suitable gain matrix with special conditions then the master system is synchronized with any chaotic dynamical system of the same dimension. With the help of this study we developed generalized theorems for synchronization of n-dimension dynamical systems for integer as well as fractional versions. it proposed that this investigation will contribute a lot to control dynamical systems and only a suitable gain matrix with special conditions is enough to synchronize the system under consideration with any other chaotic system of the same dimension. Chaotic properties of fractional version of the new finance system are also analyzed at fractional order q=0.87. Simulations results, where required, also provided for authenticity of analytical study. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=complex%20analysis" title="complex analysis">complex analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=chaos" title=" chaos"> chaos</a>, <a href="https://publications.waset.org/abstracts/search?q=generalized%20synchronization" title=" generalized synchronization"> generalized synchronization</a>, <a href="https://publications.waset.org/abstracts/search?q=control%20dynamics" title=" control dynamics"> control dynamics</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%20order%20analysis" title=" fractional order analysis"> fractional order analysis</a> </p> <a href="https://publications.waset.org/abstracts/182892/chaos-analysis-of-a-3d-finance-system-and-generalized-synchronization-for-n-dimension" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/182892.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">69</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10821</span> An Analytical Study of FRP-Concrete Bridge Superstructures</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Wael%20I.%20Alnahhal">Wael I. Alnahhal</a> </p> <p class="card-text"><strong>Abstract:</strong></p> It is a major challenge to build a bridge superstructure that has long-term durability and low maintenance requirements. A solution to this challenge may be to use new materials or to implement new structural systems. Fiber reinforced polymer (FRP) composites have continued to play an important role in solving some of persistent problems in infrastructure applications because of its high specific strength, light weight, and durability. In this study, the concept of the hybrid FRP-concrete structural systems is applied to a bridge superstructure. The hybrid FRP-concrete bridge superstructure is intended to have durable, structurally sound, and cost effective hybrid system that will take full advantage of the inherent properties of both FRP materials and concrete. In this study, two hybrid FRP-concrete bridge systems were investigated. The first system consists of trapezoidal cell units forming a bridge superstructure. The second one is formed by arch cells. The two systems rely on using cellular components to form the core of the bridge superstructure, and an outer shell to warp around those cells to form the integral unit of the bridge. Both systems were investigated analytically by using finite element (FE) analysis. From the rigorous FE studies, it was concluded that first system is more efficient than the second. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=bridge%20superstructure" title="bridge superstructure">bridge superstructure</a>, <a href="https://publications.waset.org/abstracts/search?q=hybrid%20system" title=" hybrid system"> hybrid system</a>, <a href="https://publications.waset.org/abstracts/search?q=fiber%20reinforced%20polymer" title=" fiber reinforced polymer"> fiber reinforced polymer</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20element%20analysis" title=" finite element analysis"> finite element analysis</a> </p> <a href="https://publications.waset.org/abstracts/28411/an-analytical-study-of-frp-concrete-bridge-superstructures" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/28411.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">335</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10820</span> Hydrogen: Contention-Aware Hybrid Memory Management for Heterogeneous CPU-GPU Architectures</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Yiwei%20Li">Yiwei Li</a>, <a href="https://publications.waset.org/abstracts/search?q=Mingyu%20Gao"> Mingyu Gao</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Integrating hybrid memories with heterogeneous processors could leverage heterogeneity in both compute and memory domains for better system efficiency. To ensure performance isolation, we introduce Hydrogen, a hardware architecture to optimize the allocation of hybrid memory resources to heterogeneous CPU-GPU systems. Hydrogen supports efficient capacity and bandwidth partitioning between CPUs and GPUs in both memory tiers. We propose decoupled memory channel mapping and token-based data migration throttling to enable flexible partitioning. We also support epoch-based online search for optimized configurations and lightweight reconfiguration with reduced data movements. Hydrogen significantly outperforms existing designs by 1.21x on average and up to 1.31x. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=hybrid%20memory" title="hybrid memory">hybrid memory</a>, <a href="https://publications.waset.org/abstracts/search?q=heterogeneous%20systems" title=" heterogeneous systems"> heterogeneous systems</a>, <a href="https://publications.waset.org/abstracts/search?q=dram%20cache" title=" dram cache"> dram cache</a>, <a href="https://publications.waset.org/abstracts/search?q=graphics%20processing%20units" title=" graphics processing units"> graphics processing units</a> </p> <a href="https://publications.waset.org/abstracts/183187/hydrogen-contention-aware-hybrid-memory-management-for-heterogeneous-cpu-gpu-architectures" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/183187.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">97</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10819</span> The Potential of 48V HEV in Real Driving Operation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mark%20Schudeleit">Mark Schudeleit</a>, <a href="https://publications.waset.org/abstracts/search?q=Christian%20Sieg"> Christian Sieg</a>, <a href="https://publications.waset.org/abstracts/search?q=Ferit%20K%C3%BC%C3%A7%C3%BCkay"> Ferit Küçükay</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This publication focuses on the limits and potentials of 48V hybrid systems, which are especially due to the cost advantages an attractive alternative, compared to established high volt-age HEVs and thus will gain relevant market shares in the future. Firstly, at market overview is given which shows the current known 48V hybrid concepts and demonstrators. These topologies will be analyzed and evaluated regarding the system power and the battery capacity as well as their implemented hybrid functions. The potential in fuel savings and CO2 reduction is calculated followed by the customer-relevant dimensioning of the electric motor and the battery. For both measured data of the real customer operation is used. Subsequently, the CO2 saving potentials of the customer-oriented dimensioned powertrain will be presented for the NEDC and the customer operation. With a comparison of the newly defined drivetrain with existing 48V systems the question can be answered whether current systems are dimensioned optimally for the customer operation or just for legislated driving cycles. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=48V%20hybrid%20systems" title="48V hybrid systems">48V hybrid systems</a>, <a href="https://publications.waset.org/abstracts/search?q=market%20comparison" title=" market comparison"> market comparison</a>, <a href="https://publications.waset.org/abstracts/search?q=requirements%20and%20potentials%20in%20customer%20operation" title=" requirements and potentials in customer operation"> requirements and potentials in customer operation</a>, <a href="https://publications.waset.org/abstracts/search?q=customer-oriented%20dimensioning" title=" customer-oriented dimensioning"> customer-oriented dimensioning</a>, <a href="https://publications.waset.org/abstracts/search?q=CO2%20savings" title=" CO2 savings"> CO2 savings</a> </p> <a href="https://publications.waset.org/abstracts/30122/the-potential-of-48v-hev-in-real-driving-operation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/30122.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">550</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10818</span> Hybrid Subspace Approach for Time Delay Estimation in MIMO Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mojtaba%20Saeedinezhad">Mojtaba Saeedinezhad</a>, <a href="https://publications.waset.org/abstracts/search?q=Sarah%20Yousefi"> Sarah Yousefi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we present a hybrid subspace approach for Time Delay Estimation (TDE) in multivariable systems. While several methods have been proposed for time delay estimation in SISO systems, delay estimation in MIMO systems were always a big challenge. In these systems the existing TDE methods have significant limitations because most of procedures are just based on system response estimation or correlation analysis. We introduce a new hybrid method for TDE in MIMO systems based on subspace identification and explicit output error method; and compare its performance with previously introduced procedures in presence of different noise levels and in a statistical manner. Then the best method is selected with multi objective decision making technique. It is shown that the performance of new approach is much better than the existing methods, even in low signal-to-noise conditions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=system%20identification" title="system identification">system identification</a>, <a href="https://publications.waset.org/abstracts/search?q=time%20delay%20estimation" title=" time delay estimation"> time delay estimation</a>, <a href="https://publications.waset.org/abstracts/search?q=ARX" title=" ARX"> ARX</a>, <a href="https://publications.waset.org/abstracts/search?q=OE" title=" OE"> OE</a>, <a href="https://publications.waset.org/abstracts/search?q=merit%20ratio" title=" merit ratio"> merit ratio</a>, <a href="https://publications.waset.org/abstracts/search?q=multi%20variable%20decision%20making" title=" multi variable decision making"> multi variable decision making</a> </p> <a href="https://publications.waset.org/abstracts/48722/hybrid-subspace-approach-for-time-delay-estimation-in-mimo-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/48722.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">346</span> </span> </div> </div> <ul class="pagination"> <li class="page-item disabled"><span class="page-link">&lsaquo;</span></li> <li class="page-item active"><span class="page-link">1</span></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=hybrid%20dynamical%20systems&page=2">2</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=hybrid%20dynamical%20systems&page=3">3</a></li> <li class="page-item"><a class="page-link" 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