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Suboptimal Control for Nonlinear Systems with Disturbance via Integral Sliding Mode Control and Policy Iteration

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  • Yuqing Zheng

    (Tianjin University)

  • Guoshan Zhang

    (Tianjin University)

Abstract

In this paper, we consider a suboptimal control problem for nonlinear systems with unmatched disturbance via integral sliding mode control and policy iteration. Firstly, the unmatched disturbance is estimated by a nonlinear disturbance observer. Secondly, the integral sliding mode controller based on the disturbance estimation is designed to guarantee the reachability of the sliding-mode surface. Furthermore, the policy iteration approach based on actor-critic neural networks is used to design the suboptimal controller, which can achieve the desired performance. Finally, the effectiveness of the proposed approach is demonstrated through simulation examples.

Suggested Citation

  • Yuqing Zheng & Guoshan Zhang, 2020. "Suboptimal Control for Nonlinear Systems with Disturbance via Integral Sliding Mode Control and Policy Iteration," Journal of Optimization Theory and Applications, Springer, vol. 185(2), pages 652-677, May.
    • Handle: RePEc:spr:joptap:v:185:y:2020:i:2:d:10.1007_s10957-020-01652-7
    DOI: 10.1007/s10957-020-01652-7
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    References listed on IDEAS

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    1. Jiaxing Che & Michael Santone & Chengyu Cao, 2015. "Adaptive Control for Systems with Output Constraints Using an Online Optimization Method," Journal of Optimization Theory and Applications, Springer, vol. 165(2), pages 480-506, May.
    2. Wang, Jinhuan & Xu, Yuling & Xu, Yong & Yang, Dedong, 2019. "Time-varying formation for high-order multi-agent systems with external disturbances by event-triggered integral sliding mode control," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 333-343.
    3. Shalabh Bhatnagar & K. Lakshmanan, 2012. "An Online Actor–Critic Algorithm with Function Approximation for Constrained Markov Decision Processes," Journal of Optimization Theory and Applications, Springer, vol. 153(3), pages 688-708, June.
    4. G. Gnecco & M. Sanguineti, 2010. "Suboptimal Solutions to Dynamic Optimization Problems via Approximations of the Policy Functions," Journal of Optimization Theory and Applications, Springer, vol. 146(3), pages 764-794, September.
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