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Finite-time stabilization for a class of nonlinear systems via optimal control

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  • Zhang, Yu
  • Feng, Zhi Guo
  • Yang, Xinsong
  • Alsaadi, Fuad E.
  • Ahmad, Bashir

Abstract

In general, finite-time stabilization techniques can always stabilize a system if control cost is not considered. Considering the fact that control cost is a very important factor in control area, we investigate finite-time stabilization problem for a class of nonlinear systems in this paper, where the control cost can also be reduced. We formulate this problem into an optimal control problem, where the control functions are optimized such that the system can be stabilized with minimum control cost. Then, the control parameterization enhancing transform and the control parameterization method are applied to solve this problem. Two numerical examples are illustrated to show the effectiveness of the proposed method.

Suggested Citation

  • Zhang, Yu & Feng, Zhi Guo & Yang, Xinsong & Alsaadi, Fuad E. & Ahmad, Bashir, 2018. "Finite-time stabilization for a class of nonlinear systems via optimal control," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 146(C), pages 14-26.
    • Handle: RePEc:eee:matcom:v:146:y:2018:i:c:p:14-26
    DOI: 10.1016/j.matcom.2017.09.003
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    References listed on IDEAS

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    1. Cao, Jinde & Wang, Zidong & Sun, Yonghui, 2007. "Synchronization in an array of linearly stochastically coupled networks with time delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(2), pages 718-728.
    2. Botmart, Thongchai & Niamsup, Piyapong, 2007. "Adaptive control and synchronization of the perturbed Chua’s system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 75(1), pages 37-55.
    3. Salarieh, Hassan & Alasty, Aria, 2008. "Adaptive chaos synchronization in Chua's systems with noisy parameters," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 233-241.
    4. Xu, Bingji & Xu, Yuan & He, Linman, 2012. "LMI-based stability analysis of impulsive high-order Hopfield-type neural networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 86(C), pages 67-77.
    5. Wang, Dan & Huang, Jialiang & Lan, Weiyao & Li, Xiaoqiang, 2009. "Neural network-based robust adaptive control of nonlinear systems with unmodeled dynamics," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(5), pages 1745-1753.
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    Cited by:

    1. Mathiyalagan, K. & Ragul, R., 2022. "Observer-based finite-time dissipativity for parabolic systems with time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 413(C).
    2. Zhang, Wanli & Yang, Xinsong & Yang, Shiju & Alsaedi, Ahmed, 2021. "Finite-time and fixed-time bipartite synchronization of complex networks with signed graphs," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 319-329.
    3. Zhou, Ya & Wan, Xiaoxiao & Huang, Chuangxia & Yang, Xinsong, 2020. "Finite-time stochastic synchronization of dynamic networks with nonlinear coupling strength via quantized intermittent control," Applied Mathematics and Computation, Elsevier, vol. 376(C).

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