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Fixed-time optimized control for nonlinear strict-feedback systems based on reinforcement learning and disturbance observer

Author

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  • Gao, Dong-Xiang
  • Cui, Wen-Hua
  • Wu, Li-Bing
  • Zhang, Yu-Jun
  • Tao, Ye

Abstract

The present study focuses on the fixed-time optimal control problem for a class of nonlinear strict-feedback systems subject to unknown external disturbances. First, a fuzzy state and disturbance observer is developed to estimate both unmeasurable states and external disturbances. To further improve estimation accuracy of external disturbances, a novel intermediate variable estimator incorporating a time-varying gain parameter is introduced. Subsequently, based on the disturbance-observer-critic-actor (DOCA) reinforcement learning architecture, a fixed-time optimal control strategy is proposed by integrating fuzzy approximation and backstepping techniques. This approach ensures optimality in both virtual and actual control of the controlled system while guaranteeing its fixed-time stability. Finally, the effectiveness of the proposed strategy is validated through theoretical and simulation studies.

Suggested Citation

  • Gao, Dong-Xiang & Cui, Wen-Hua & Wu, Li-Bing & Zhang, Yu-Jun & Tao, Ye, 2026. "Fixed-time optimized control for nonlinear strict-feedback systems based on reinforcement learning and disturbance observer," Applied Mathematics and Computation, Elsevier, vol. 508(C).
    • Handle: RePEc:eee:apmaco:v:508:y:2026:i:c:s0096300325003546
    DOI: 10.1016/j.amc.2025.129628
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    References listed on IDEAS

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    1. Ma, Haoxiang & Xiong, Shixun & Fu, Zhumu & Tao, Fazhan & Ji, Baofeng, 2024. "High-order disturbance observer-based safe tracking control for a class of uncertain MIMO nonlinear systems with time-varying full state constraints," Applied Mathematics and Computation, Elsevier, vol. 466(C).
    2. Yang, Lei & Nagy, Zoltan & Goffin, Philippe & Schlueter, Arno, 2015. "Reinforcement learning for optimal control of low exergy buildings," Applied Energy, Elsevier, vol. 156(C), pages 577-586.
    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).
    4. Wang, Huanqing & Meng, Zhu, 2024. "Fixed-time adaptive neural tracking control for high-order nonlinear switched systems with input saturation and dead-zone," Applied Mathematics and Computation, Elsevier, vol. 480(C).
    5. Xu, Ke & Wang, Huanqing & Liu, Peter Xiaoping, 2023. "Adaptive fuzzy finite-time tracking control of nonlinear systems with unmodeled dynamics," Applied Mathematics and Computation, Elsevier, vol. 450(C).
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    1. Wu, Ziwei & Xu, Ning & Zhang, Liang & Zhao, Ning & Song, Guangjing, 2026. "Privacy preservation-based dynamic event-triggered bipartite consensus strategy for nonlinear multi-agent systems with unknown mismatched disturbances," Applied Mathematics and Computation, Elsevier, vol. 515(C).

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