Document Zbl 07892392

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Control</a> <a href="/?q=in%3A515656" title="Articles in this Issue">25, No. 5, 3456-3473 (2023)</a>. </div> <div class="abstract">Summary: This paper investigates a fixed-time convergence issue using the sliding mode observer-based controller for a class of uncertain nonlinear double integrator systems. This observer-based controller is designed assuming that only the first state measurement is available and there is no information about external disturbances and modeling uncertainties. A new form of sliding mode observer in combination with a sliding mode controller is designed to estimate unmeasured state and unknown disturbances and uncertainties as well as provide the estimated data in the control law. A novel form of sliding surfaces for the robust observer-based controller is proposed for which fixed-time convergence is guaranteed to achieve trajectory tracking. In the proposed fixed-time scheme, the bound on the settling time is user-defined using design parameters regardless of the system’s initial conditions. The control law and observer law are designed such that the chattering issue is alleviated in the control signal. The stability analysis of the closed-loop system using the observer-based controller is established via the Lyapunov theory. The validity of the controller design is tested by applying and simulating an example of a robot manipulator in Simulink/MATLAB. The superiority of the proposed method is demonstrated by comparing it with two other methods from the relevant literature.<br class="zbmathjax-paragraph">© 2023 The Authors. <span class="zbmathjax-textit">Asian Journal of Control</span> published by John Wiley & Sons Australia, Ltd on behalf of Chinese Automatic Control Society.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7892392">Cited in <strong>5</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A93C10" title="MSC2020">93C10</a> </td> <td class="space"> Nonlinear systems in control theory </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93B12" title="MSC2020">93B12</a> </td> <td class="space"> Variable structure systems </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93D40" title="MSC2020">93D40</a> </td> <td class="space"> Finite-time stability </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Achattering-free">chattering-free</a>; <a href="/?q=ut%3Afixed-time+stability">fixed-time stability</a>; <a href="/?q=ut%3ALyapunov+stability">Lyapunov stability</a>; <a href="/?q=ut%3Asliding+mode+controller">sliding mode controller</a>; <a href="/?q=ut%3Asliding+mode+observer">sliding mode observer</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 07892392" data-ciurl="/ci/07892392" data-biburl="/bibtex/07892392.bib" data-amsurl="/amsrefs/07892392.bib" data-xmlurl="/xml/07892392.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07892392.pdf" title="Zbl 07892392 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1002/asjc.3052" aria-label="DOI for “Fixed-time sliding mode observer-based controller for a class of uncertain nonlinear double integrator systems”" title="10.1002/asjc.3052">DOI</a> </div> <div class="sfx" style="float: right;"> <a href="https://creativecommons.org/licenses/by-nc-nd/4.0/" target="_blank" title="Open Access License" class="cc-license-link no-new-tab-icon"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/cc.svg" alt="Creative Commons CC license icon" class="cc-license-icon"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/by.svg" alt="Creative Commons BY license icon" class="cc-license-icon"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/nc.svg" alt="Creative Commons NC license icon" class="cc-license-icon"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/nd.svg" alt="Creative Commons ND license icon" class="cc-license-icon"> </a> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Min, H.; Xu, S.; Li, Y.; Chu, Y.; Wei, Y.; Zhang, Z., Adaptive finite‐time control for stochastic nonlinear systems subject to unknown covariance noise, J. Franklin Inst., 355, 2645-2661, 2018 · <a href="/1393.93137" class="nowrap">Zbl 1393.93137</a></td> </tr><tr> <td>[2]</td> <td class="space">Isidori, A., Nonlinear control systems, 2013, Springer Science & Business Media · <a href="/0569.93034" class="nowrap">Zbl 0569.93034</a></td> </tr><tr> <td>[3]</td> <td class="space">Krstic, M.; Kanellakopoulos, I.; Kokotovic, P. V., Nonlinear and adaptive control design, 1995, Wiley · <a href="/0763.93043" class="nowrap">Zbl 0763.93043</a></td> </tr><tr> <td>[4]</td> <td class="space">Sontag, E. D., Input to state stability: Basic concepts and results, Nonlinear and optimal control theory, 163-220, 2008, Springer · <a href="/1175.93001" class="nowrap">Zbl 1175.93001</a></td> </tr><tr> <td>[5]</td> <td class="space">Yu, S.; Yu, X.; Shirinzadeh, B.; Man, Z., Continuous finite‐time control for robotic manipulators with terminal sliding mode, Automatica, 41, 11, 1957-1964, 2005 · <a href="/1125.93423" class="nowrap">Zbl 1125.93423</a></td> </tr><tr> <td>[6]</td> <td class="space">Elsayed, B. A.; Hassan, M.; Mekhilef, S., Decoupled third‐order fuzzy sliding model control for cart‐inverted pendulum system, Appl. Math, 7, 1, 193-201, 2013</td> </tr><tr> <td>[7]</td> <td class="space">Hong, Y.; Wang, H. O.; Bushnell, L. G., Adaptive finite‐time control of nonlinear systems, 2001</td> </tr><tr> <td>[8]</td> <td class="space">Sun, M.; Chen, J.; Li, H., Finite‐time adaptive robust control, 2017</td> </tr><tr> <td>[9]</td> <td class="space">Cao, Y.; Stuart, D.; Ren, W.; Meng, Z., Distributed containment control for multiple autonomous vehicles with double‐integrator dynamics: Algorithms and experiments, IEEE Trans. Control Syst. Technol., 19, 4, 929-938, 2011</td> </tr><tr> <td>[10]</td> <td class="space">He, W.; Zhang, S.; Ge, S. S., Adaptive control of a flexible crane system with the boundary output constraint, IEEE Trans. Ind. Electron., 61, 8, 4126-4133, 2014</td> </tr><tr> <td>[11]</td> <td class="space">Kchaou, A.; Ayadi, A.; Naamane, A.; M’Sirdi, N.; Koubaa, Y., An adaptive sliding mode control based maximum power point tracking method for a PV stand‐alone system, 2017</td> </tr><tr> <td>[12]</td> <td class="space">Wang, F.; Liu, P. X.; Shi, P., Adaptive neural network finite‐time output feedback control of quantized nonlinear systems, IEEE Trans. Cybern., 47, 2568-2578, 2017</td> </tr><tr> <td>[13]</td> <td class="space">Wang, X.; Li, S.; Shi, P., Distributed finite‐time containment control for double‐integrator multiagent systems, IEEE Trans. Cybern., 44, 9, 1518-1528, 2014</td> </tr><tr> <td>[14]</td> <td class="space">Huang, B.; Li, A.; Guo, Y.; Wang, C.; Zhang, Y., Adaptive backstepping finite‐time attitude tracking control of spacecraft without unwinding, 2017</td> </tr><tr> <td>[15]</td> <td class="space">Hong, Y.; Wang, J.; Cheng, D., Adaptive finite‐time control of nonlinear systems with parametric uncertainty, IEEE Trans. Automat. Contr., 51, 5, 858-862, 2006 · <a href="/1366.93290" class="nowrap">Zbl 1366.93290</a></td> </tr><tr> <td>[16]</td> <td class="space">Tran, X.‐T.; Kang, H.‐J., A novel adaptive finite‐time control method for a class of uncertain nonlinear systems, Int. J. Precis. Eng. Manuf., 16, 13, 2647-2654, 2015</td> </tr><tr> <td>[17]</td> <td class="space">Ginoya, D.; Shendge, P.; Phadke, S., Sliding mode control for mismatched uncertain systems using an extended disturbance observer, IEEE Trans. Ind. Electron., 61, 4, 1983-1992, 2014</td> </tr><tr> <td>[18]</td> <td class="space">Alinaghi Hosseinabadi, P.; Soltani Sharif Abadi, A.; Mekhilef, S.; Pota, H. R., Two novel approaches of adaptive finite‐time sliding mode control for a class of single‐input multiple‐output uncertain nonlinear systems, IET Cyber‐Syst. Robot., 3, 2, 173-183, 2021</td> </tr><tr> <td>[19]</td> <td class="space">Li, F.; Wu, L.; Shi, P.; Lim, C. C., State estimation and sliding mode control for semi‐Markovian jump systems with mismatched uncertainties, Automatica, 51, 385-393, 2015 · <a href="/1309.93157" class="nowrap">Zbl 1309.93157</a></td> </tr><tr> <td>[20]</td> <td class="space">Li, H.; Shi, P.; Yao, D.; Wu, L., Observer‐based adaptive sliding mode control for nonlinear Markovian jump systems, Automatica, 64, 133-142, 2016 · <a href="/1329.93126" class="nowrap">Zbl 1329.93126</a></td> </tr><tr> <td>[21]</td> <td class="space">Lu, X.; Schwartz, H. M., A revised adaptive fuzzy sliding mode controller for robotic manipulators, Int. J. Model. Identif. Contr., 4, 2, 127-133, 2008</td> </tr><tr> <td>[22]</td> <td class="space">Hassrizal, H.; Rossiter, J., Application of decaying boundary layer and switching function method thorough error feedback for sliding mode control on spacecraft’s attitude, 2017</td> </tr><tr> <td>[23]</td> <td class="space">Utkin, V. I., Sliding modes in control and optimization, 2013, Springer Science & Business Media</td> </tr><tr> <td>[24]</td> <td class="space">Elsayed, B. A.; Hassan, M. A.; Mekhilef, S., Fuzzy swinging‐up with sliding mode control for third order cart‐inverted pendulum system, Int. J. Contr. Automat. Syst., 13, 1, 238-248, 2015</td> </tr><tr> <td>[25]</td> <td class="space">Li, H.; Shi, P.; Yao, D., Adaptive sliding‐mode control of Markov jump nonlinear systems with actuator faults, IEEE Trans. Automat. Contr., 62, 4, 1933-1939, 2017 · <a href="/1366.93718" class="nowrap">Zbl 1366.93718</a></td> </tr><tr> <td>[26]</td> <td class="space">Baek, J.; Jin, M.; Han, S., A new adaptive sliding‐mode control scheme for application to robot manipulators, IEEE Trans. Ind. Electron., 63, 6, 3628-3637, 2016</td> </tr><tr> <td>[27]</td> <td class="space">Yu, X.; Man, Z., Model reference adaptive control systems with terminal sliding modes, Int. J. Contr., 64, 6, 1165-1176, 1996 · <a href="/0864.93068" class="nowrap">Zbl 0864.93068</a></td> </tr><tr> <td>[28]</td> <td class="space">Yang, Y.; Hua, C.; Guan, X., Adaptive fuzzy finite‐time coordination control for networked nonlinear bilateral teleoperation system, IEEE Trans. Fuzzy Syst., 22, 3, 631-641, 2014</td> </tr><tr> <td>[29]</td> <td class="space">Lu, K.; Xia, Y.; Yu, C.; Liu, H., Finite‐time tracking control of rigid spacecraft under actuator saturations and faults, IEEE Trans. Automat. Sci. Eng., 13, 1, 368-381, 2016</td> </tr><tr> <td>[30]</td> <td class="space">Zhihong, M.; O’Day, M.; Yu, X., A robust adaptive terminal sliding mode control for rigid robotic manipulators, J. Intell. Robot. Syst., 24, 1, 23-41, 1999 · <a href="/0963.93065" class="nowrap">Zbl 0963.93065</a></td> </tr><tr> <td>[31]</td> <td class="space">Zhang, H.; Xu, N.; Zong, G.; Alkhateeb, A. F., Adaptive fuzzy hierarchical sliding mode control of uncertain under‐actuated switched nonlinear systems with actuator faults, Int. J. Syst. Sci., 52, 8, 1499-1514, 2021 · <a href="/1483.93325" class="nowrap">Zbl 1483.93325</a></td> </tr><tr> <td>[32]</td> <td class="space">Liu, S.; Zhang, L.; Niu, B.; Zhao, X.; Ahmad, A. M., Adaptive neural finite‐time hierarchical sliding mode control of uncertain under‐actuated switched nonlinear systems with backlash‐like hysteresis, Inform. Sci., 599, 147-169, 2022 · <a href="/1533.93366" class="nowrap">Zbl 1533.93366</a></td> </tr><tr> <td>[33]</td> <td class="space">Zhang, H.; Wang, H.; Niu, B.; Zhang, L.; Ahmad, A. M., Sliding‐mode surface‐based adaptive actor‐critic optimal control for switched nonlinear systems with average dwell time, Inform. Sci., 580, 756-774, 2021 · <a href="/07786227" class="nowrap">Zbl 07786227</a></td> </tr><tr> <td>[34]</td> <td class="space">Gauthier, J. P.; Hammouri, H.; Othman, S., A simple observer for nonlinear systems applications to bioreactors, IEEE Trans. Automat. Contr, 37, 6, 875-880, 1992 · <a href="/0775.93020" class="nowrap">Zbl 0775.93020</a></td> </tr><tr> <td>[35]</td> <td class="space">Hou, M.; Muller, P., Design of observers for linear systems with unknown inputs, IEEE Trans. Automat. Contr, 37, 6, 871-875, 1992 · <a href="/0775.93021" class="nowrap">Zbl 0775.93021</a></td> </tr><tr> <td>[36]</td> <td class="space">Moraal, P.; Grizzle, J., Observer design for nonlinear systems with discrete‐time measurements, IEEE Trans. Automat. Contr, 40, 3, 395-404, 1995 · <a href="/0821.93014" class="nowrap">Zbl 0821.93014</a></td> </tr><tr> <td>[37]</td> <td class="space">Zhang, H.; Wang, J., Adaptive sliding‐mode observer design for a selective catalytic reduction system of ground‐vehicle diesel engines, IEEE/ASME Trans. Mechatron., 21, 4, 2027-2038, 2016</td> </tr><tr> <td>[38]</td> <td class="space">Fradkov, A.; Nijmeijer, H.; Markov, A., Adaptive observer‐based synchronization for communication, Int. J. Bifurcat. Chaos, 10, 12, 2807-2813, 2000 · <a href="/0972.93005" class="nowrap">Zbl 0972.93005</a></td> </tr><tr> <td>[39]</td> <td class="space">Mascolo, S.; Grassi, G., Controlling chaos via backstepping design, Phys. Rev. E, 56, 5, 6166-6169, 1997</td> </tr><tr> <td>[40]</td> <td class="space">López‐Mancilla, D.; Cruz‐Hernández, C.; Posadas‐Castillo, C., A modified chaos‐based communication scheme using Hamiltonian forms and observer, Journal of Physics: Conference Series, 23, 267-275, 2005</td> </tr><tr> <td>[41]</td> <td class="space">Carroll, T. L.; Pecora, L. M., Synchronizing chaotic circuits, IEEE Trans. Circuit Syst., 38, 4, 453-456, 1991</td> </tr><tr> <td>[42]</td> <td class="space">Grassi, G.; Mascolo, S., Nonlinear observer design to synchronize hyperchaotic systems via a scalar signal, IEEE Trans. Circuit Syst. I: Fundamental Theory Appl., 44, 10, 1011-1014, 1997</td> </tr><tr> <td>[43]</td> <td class="space">Arcak, M.; Kokotović, P., Nonlinear observers: A circle criterion design and robustness analysis, Automatica, 37, 12, 1923-1930, 2001 · <a href="/0996.93010" class="nowrap">Zbl 0996.93010</a></td> </tr><tr> <td>[44]</td> <td class="space">Huangfu, Y.; Xu, J. N.; Zhuo, S. R.; Xie, M. C.; Liu, Y. T., A novel adaptive sliding mode observer for SOC estimation of lithium batteries in electric vehicles, 2017</td> </tr><tr> <td>[45]</td> <td class="space">Chang, X.‐H.; Jin, X., Observer‐based fuzzy feedback control for nonlinear systems subject to transmission signal quantization, Appl. Math Comput., 414, 2022 · <a href="/1510.93242" class="nowrap">Zbl 1510.93242</a></td> </tr><tr> <td>[46]</td> <td class="space">Alinaghi Hosseinabadi, P.; Soltani Sharif Abadi, A.; Mekhilef, S.; Pota, H. R., Fixed‐time adaptive robust synchronization with a state observer of chaotic support structures for offshore wind turbines, J. Contr. Automat. Electr. Syst., 32, 4, 942-955, 2021</td> </tr><tr> <td>[47]</td> <td class="space">Polyakov, A., Nonlinear feedback design for fixed‐time stabilization of linear control systems, IEEE Trans. Automat. Contr, 57, 8, 2106-2110, 2011 · <a href="/1369.93128" class="nowrap">Zbl 1369.93128</a></td> </tr><tr> <td>[48]</td> <td class="space">Li, H.; Liao, X.; Huang, T.; Zhu, W., Event‐triggering sampling based leader‐following consensus in second‐order multi‐agent systems, IEEE Trans. Automat. Contr, 60, 7, 1998-2003, 2014 · <a href="/1360.93031" class="nowrap">Zbl 1360.93031</a></td> </tr><tr> <td>[49]</td> <td class="space">Alinaghi Hosseinabadi, P.; Ordys, A.; Soltani Sharif Abadi, A.; Mekhilef, S.; Pota, H. R., State and disturbance observers‐based chattering‐free fixed‐time sliding mode control for a class of high‐order nonlinear systems, Adv. Contr. Appl.: Eng. Ind. Syst., 3, 3, 2021</td> </tr><tr> <td>[50]</td> <td class="space">Zuo, Z., Non‐singular fixed‐time terminal sliding mode control of non‐linear systems, IET Contr. Theory Appl., 9, 4, 545-552, 2014</td> </tr><tr> <td>[51]</td> <td class="space">Feng, Y.; Yu, X.; Man, Z., Non‐singular terminal sliding mode control of rigid manipulators, Automatica, 38, 12, 2159-2167, 2002 · <a href="/1015.93006" class="nowrap">Zbl 1015.93006</a></td> </tr><tr> <td>[52]</td> <td class="space">Yu, X.; Zhihong, M., Fast terminal sliding‐mode control design for nonlinear dynamical systems, IEEE Trans. Circuit Syst. I: Fundamental Theory Appl., 49, 2, 261-264, 2002 · <a href="/1368.93213" class="nowrap">Zbl 1368.93213</a></td> </tr><tr> <td>[53]</td> <td class="space">Yang, J.; Li, S.; Yu, X., Sliding‐mode control for systems with mismatched uncertainties via a disturbance observer, IEEE Trans. Ind. Electron., 60, 1, 160-169, 2012</td> </tr><tr> <td>[54]</td> <td class="space">Castillo‐García, P.; Muñoz Hernandez, L. E.; García Gil, P.; P. Castillo‐García (ed.); L. E. M. Hernandez (ed.); P. G. Gil (ed.), Mode control**This chapter was developed in collaboration with Efrain Ibarra from the Laboratoire Heudiasyc at the Université de Technologie de Compiegne in France and with M. Jimenez from the Universidad Autonoma de Nuevo Leon in Mexico, Indoor navigation strategies for aerial autonomous systems, 179, 2017, Butterworth‐Heinemann</td> </tr><tr> <td>[55]</td> <td class="space">Benosman, M.; Lum, K., Passive actuators’ fault‐tolerant control for affine nonlinear systems, IEEE Trans. Contr. Syst. Technol., 18, 1, 152-163, 2010</td> </tr><tr> <td>[56]</td> <td class="space">Yang, L.; Yang, J., Nonsingular fast terminal sliding‐mode control for nonlinear dynamical systems, Int. J. Robust Nonlin. Contr., 21, 16, 1865-1879, 2011 · <a href="/1237.93039" class="nowrap">Zbl 1237.93039</a></td> </tr><tr> <td>[57]</td> <td class="space">Xing, L.; Wen, C.; Liu, Z.; Su, H.; Cai, J., Event‐triggered adaptive control for a class of uncertain nonlinear systems, IEEE Trans. Automat. Contr, 62, 4, 2071-2076, 2017 · <a href="/1366.93305" class="nowrap">Zbl 1366.93305</a></td> </tr><tr> <td>[58]</td> <td class="space">Liu, Z.; Lai, G.; Zhang, Y.; Chen, C. L. P., Adaptive fuzzy tracking control of nonlinear time‐delay systems with dead‐zone output mechanism based on a novel smooth model, IEEE Trans. Fuzzy Syst., 23, 6, 1998-2011, 2015</td> </tr><tr> <td>[59]</td> <td class="space">Yi, S.; Zhai, J., Adaptive second‐order fast nonsingular terminal sliding mode control for robotic manipulators, ISA Trans., 90, 41-51, 2019</td> </tr><tr> <td>[60]</td> <td class="space">Ríos, H.; Teel, A. R., A hybrid fixed‐time observer for state estimation of linear systems, Automatica, 87, 103-112, 2018 · <a href="/1378.93026" class="nowrap">Zbl 1378.93026</a></td> </tr><tr> <td>[61]</td> <td class="space">Garg, K.; Panagou, D., Fixed‐time stable gradient flows: Applications to continuous‐time optimization, IEEE Trans. Automat. Contr, 66, 5, 2002-2015, 2021 · <a href="/1536.93756" class="nowrap">Zbl 1536.93756</a></td> </tr><tr> <td>[62]</td> <td class="space">Zimenko, K.; Polyakov, A.; Efimov, D.; Perruquetti, W., On simple scheme of finite/fixed‐time control design, Int. J. Contr., 93, 6, 1353-1361, 2020 · <a href="/1443.93124" class="nowrap">Zbl 1443.93124</a></td> </tr><tr> <td>[63]</td> <td class="space">Zuo, Z., Nonsingular fixed‐time consensus tracking for second‐order multi‐agent networks, Automatica, 54, 305-309, 2015 · <a href="/1318.93010" class="nowrap">Zbl 1318.93010</a></td> </tr><tr> <td>[64]</td> <td class="space">Zuo, Z.; Tie, L., A new class of finite‐time nonlinear consensus protocols for multi‐agent systems, Int. J. Contr., 87, 2, 363-370, 2014 · <a href="/1317.93027" class="nowrap">Zbl 1317.93027</a></td> </tr><tr> <td>[65]</td> <td class="space">Yao, Q., Fixed‐time trajectory tracking control for unmanned surface vessels in the presence of model uncertainties and external disturbances, Int. J. Contr., 95, 1133-1143, 2022 · <a href="/1492.93164" class="nowrap">Zbl 1492.93164</a></td> </tr><tr> <td>[66]</td> <td class="space">Wu, D.; Du, H.; Wen, G.; Lü, J., Fixed‐time synchronization control for a class of master-slave systems based on homogeneous method, IEEE Trans. Circuit Syst. II: Exp. Br., 66, 9, 1547-1551, 2018</td> </tr><tr> <td>[67]</td> <td class="space">Basin, M. V.; Guerra‐Avellaneda, F.; Shtessel, Y. B., Stock management problem: Adaptive fixed‐time convergent continuous controller design, IEEE Trans. Syst. Man Cybern.: Syst., 50, 12, 4974-4983, 2019</td> </tr><tr> <td>[68]</td> <td class="space">Lopez‐Ramirez, F.; Efimov, D.; Polyakov, A.; Perruquetti, W., Fixed‐time output stabilization and fixed‐time estimation of a chain of integrators, Int. J. Robust Nonlin. Contr., 28, 16, 4647-4665, 2018 · <a href="/1402.93225" class="nowrap">Zbl 1402.93225</a></td> </tr><tr> <td>[69]</td> <td class="space">Li, G.; Wu, Y.; Liu, X., Adaptive fixed‐time consensus tracking control method for second‐order multi‐agent systems with disturbances, J. Franklin Inst., 357, 3, 1516-1531, 2020 · <a href="/1430.93194" class="nowrap">Zbl 1430.93194</a></td> </tr><tr> <td>[70]</td> <td class="space">Gao, F.; Zhu, C.; Huang, J.; Wu, Y., Global fixed‐time output feedback stabilization of perturbed planar nonlinear systems, IEEE Trans. Circuit Syst. II: Expr. Br., 68, 2, 707-711, 2020</td> </tr><tr> <td>[71]</td> <td class="space">Tan, J.; Guo, S., Backstepping control with fixed‐time prescribed performance for fixed wing UAV under model uncertainties and external disturbances, Int. J. Contr., 95, 934-951, 2022 · <a href="/1485.93400" class="nowrap">Zbl 1485.93400</a></td> </tr><tr> <td>[72]</td> <td class="space">Wu, Y.; Ma, F.; Liu, X.; Hua, Y.; Liu, X.; Li, G., Super twisting disturbance observer‐based fixed‐time sliding mode backstepping control for air‐breathing hypersonic vehicle, IEEE Access, 8, 17567-17583, 2020</td> </tr><tr> <td>[73]</td> <td class="space">Zhang, L.; Wang, Y.; Hou, Y.; Li, H., Fixed‐time sliding mode control for uncertain robot manipulators, IEEE Access, 7, 149750-149763, 2019</td> </tr><tr> <td>[74]</td> <td class="space">Zhang, Z.; Wu, Y., Fixed‐time regulation control of uncertain nonholonomic systems and its applications, Int. J. Contr., 90, 7, 1327-1344, 2017 · <a href="/1367.93595" class="nowrap">Zbl 1367.93595</a></td> </tr><tr> <td>[75]</td> <td class="space">Chen, C.‐C.; Sun, Z.‐Y., Fixed‐time stabilisation for a class of high‐order non‐linear systems, IET Contr. Theory Appl., 12, 18, 2578-2587, 2018</td> </tr><tr> <td>[76]</td> <td class="space">Gao, Z.; Guo, G., Command‐filtered fixed‐time trajectory tracking control of surface vehicles based on a disturbance observer, Int. J. Robust Nonlin. Contr., 29, 13, 4348-4365, 2019 · <a href="/1426.93221" class="nowrap">Zbl 1426.93221</a></td> </tr><tr> <td>[77]</td> <td class="space">Tao, M.; Chen, Q.; He, X.; Sun, M., Adaptive fixed‐time fault‐tolerant control for rigid spacecraft using a double power reaching law, Int. J. Robust Nonlin. Contr., 29, 12, 4022-4040, 2019 · <a href="/1426.93149" class="nowrap">Zbl 1426.93149</a></td> </tr><tr> <td>[78]</td> <td class="space">Jin, X., Adaptive fixed‐time control for MIMO nonlinear systems with asymmetric output constraints using universal barrier functions, IEEE Trans. Automat. Contr, 64, 7, 3046-3053, 2019 · <a href="/1478.93318" class="nowrap">Zbl 1478.93318</a></td> </tr><tr> <td>[79]</td> <td class="space">Cao, Y.; Wen, C.; Tan, S.; Song, Y., Prespecifiable fixed‐time control for a class of uncertain nonlinear systems in strict‐feedback form, Int. J. Robust Nonlin. Contr., 30, 3, 1203-1222, 2020 · <a href="/1447.93204" class="nowrap">Zbl 1447.93204</a></td> </tr><tr> <td>[80]</td> <td class="space">Shi, X.‐N.; Zhou, Z. G.; Zhou, D.; Li, R., Event‐triggered fixed‐time adaptive trajectory tracking for a class of uncertain nonlinear systems with input saturation, IEEE Trans. Circuit System II: Expr. Br., 68, 3, 983-987, 2020</td> </tr><tr> <td>[81]</td> <td class="space">Huang, Y.; Jia, Y., Adaptive fixed‐time six‐DOF tracking control for noncooperative spacecraft fly‐around mission, IEEE Trans. Contr. Syst. Technol., 27, 4, 1796-1804, 2018</td> </tr><tr> <td>[82]</td> <td class="space">Basin, M.; Panathula, C. B.; Shtessel, Y., Adaptive uniform finite‐/fixed‐time convergent second‐order sliding‐mode control, Int. J. Contr., 89, 9, 1777-1787, 2016 · <a href="/1353.93022" class="nowrap">Zbl 1353.93022</a></td> </tr><tr> <td>[83]</td> <td class="space">Andrieu, V.; Praly, L.; Astolfi, A., Homogeneous approximation, recursive observer design, and output feedback, SIAM J. Contr. Opt., 47, 4, 1814-1850, 2008 · <a href="/1165.93020" class="nowrap">Zbl 1165.93020</a></td> </tr><tr> <td>[84]</td> <td class="space">Liu, H.; Zhang, T.; Tian, X., Continuous output‐feedback finite‐time control for a class of second‐order nonlinear systems with disturbances, Int. J. Robust Nonlin. Contr., 26, 2, 218-234, 2016 · <a href="/1333.93200" class="nowrap">Zbl 1333.93200</a></td> </tr><tr> <td>[85]</td> <td class="space">Bhat, S. P.; Bernstein, D. S., Finite‐time stability of continuous autonomous systems, SIAM J. Contr. Opt., 38, 3, 751-766, 2000 · <a href="/0945.34039" class="nowrap">Zbl 0945.34039</a></td> </tr><tr> <td>[86]</td> <td class="space">Orlov, Y., Finite time stability and robust control synthesis of uncertain switched systems, SIAM J. Contr. Opt., 43, 4, 1253-1271, 2004 · <a href="/1085.93021" class="nowrap">Zbl 1085.93021</a></td> </tr><tr> <td>[87]</td> <td class="space">Parsegov, S.; Polyakov, A.; Shcherbakov, P., Fixed‐time consensus algorithm for multi‐agent systems with integrator dynamics, IFAC Proc. Vol., 46, 27, 110-115, 2013</td> </tr><tr> <td>[88]</td> <td class="space">Bhat, S. P.; Bernstein, D. S., Continuous finite‐time stabilization of the translational and rotational double integrators, IEEE Trans. Automat. Contr, 43, 5, 678-682, 1998 · <a href="/0925.93821" class="nowrap">Zbl 0925.93821</a></td> </tr><tr> <td>[89]</td> <td class="space">Zuo, Z.; Tie, L., Distributed robust finite‐time nonlinear consensus protocols for multi‐agent systems, Int. J. Syst. Sci., 47, 6, 1366-1375, 2016 · <a href="/1333.93027" class="nowrap">Zbl 1333.93027</a></td> </tr><tr> <td>[90]</td> <td class="space">Sun, X.; Chen, W., Global generalised exponential/finite‐time control for course‐keeping of ships, Int. J. Contr., 89, 6, 1169-1179, 2016 · <a href="/1338.93198" class="nowrap">Zbl 1338.93198</a></td> </tr><tr> <td>[91]</td> <td class="space">Haitao, L.; Tie, Z., Robot dynamic identification based on the immune clonal selection algorithm, J. Appl. Sci., 13, 14, 2819-2824, 2013</td> </tr><tr> <td>[92]</td> <td class="space">Liu, H.; Zhang, T., Adaptive neural network finite‐time control for uncertain robotic manipulators, J. Intell. Robot. Syst., 75, 3-4, 363-377, 2014</td> </tr><tr> <td>[93]</td> <td class="space">Mohammadi, A.; Tavakoli, M.; Marquez, H. J.; Hashemzadeh, F., Nonlinear disturbance observer design for robotic manipulators, Contr. Eng. Pract., 21, 3, 253-267, 2013</td> </tr><tr> <td>[94]</td> <td class="space">Zhao, D.; Li, S.; Zhu, Q., Output feedback terminal sliding mode control for a class of second order nonlinear systems, Asian J. Control, 15, 1, 237-247, 2013 · <a href="/1327.93112" class="nowrap">Zbl 1327.93112</a></td> </tr><tr> <td>[95]</td> <td class="space">Yang, Y.; Gao, W.; Modares, H.; Xu, C. Z., Robust actor‐critic learning for continuous‐time nonlinear systems with unmodeled dynamics, IEEE Trans. Fuzzy Syst., 30, 2101-2112, 2021</td> </tr><tr> <td>[96]</td> <td class="space">Alinaghi Hosseinabadi, P.; Pota, H.; Mekhilef, S.; Schwartz, H., Fixed‐time observer‐based control of DFIG‐based wind energy conversion systems for maximum power extraction, Int. J. Electr. Power Energy Syst., 146, 2023</td> </tr><tr> <td>[97]</td> <td class="space">Alinaghi Hosseinabadi, P.; Soltani Sharif Abadi, A.; Mekhilef, S.; Pota, H. R., Chattering‐free trajectory tracking robust predefined‐time sliding mode control for a remotely operated vehicle, J. Contr. Automat. Electr. Syst., 31, 1177-1195, 2020</td> </tr><tr> <td>[98]</td> <td class="space">Abadi, A. S. S.; Hosseinabadi, P. A.; Mekhilef, S., Fuzzy adaptive fixed‐time sliding mode control with state observer for a class of high‐order mismatched uncertain systems, Int. J. Contr. Automat. Syst., 18, 2492-2508, 2020</td> </tr><tr> <td>[99]</td> <td class="space">Song, T.; Fang, L.; Wang, H., Model‐free finite‐time terminal sliding mode control with a novel adaptive sliding mode observer of uncertain robot systems, Asian J. Control, 24, 3, 1437-1451, 2021</td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. 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