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Echo state network-based online optimal control for discrete-time nonlinear systems

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  • Liu, Chong
  • Zhang, Huaguang
  • Luo, Yanhong
  • Zhang, Kun

Abstract

This paper investigates the online optimal control problem of discrete-time nonlinear systems using echo state network (ESN)-based adaptive dynamic programming (ADP) method. An online iterative learning algorithm is proposed to solve the partial differential Hamilton–Jacobi–Bellman (HJB) equation in real time. A novel neural networks (NN) critic-actor architecture is presented using two ESNs to implement the ADP method. Then, two online learning laws of the output weights are designed for searching the optimal cost function and control policy. The stability of system and output weights is analysed using Lyapunov approach. Three simulations are given to show the feasibility and effectiveness of the designed algorithm.

Suggested Citation

  • Liu, Chong & Zhang, Huaguang & Luo, Yanhong & Zhang, Kun, 2021. "Echo state network-based online optimal control for discrete-time nonlinear systems," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    • Handle: RePEc:eee:apmaco:v:409:y:2021:i:c:s0096300321004136
    DOI: 10.1016/j.amc.2021.126324
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    References listed on IDEAS

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    1. Pahnehkolaei, Seyed Mehdi Abedi & Alfi, Alireza & Machado, J.A. Tenreiro, 2019. "Delay independent robust stability analysis of delayed fractional quaternion-valued leaky integrator echo state neural networks with QUAD condition," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 278-293.
    2. Hongjun Yang & Zhijie Liu & Shuang Zhang, 2018. "Single Parameter Adaptive Control of Unknown Nonlinear Systems with Tracking Error Constraints," Complexity, Hindawi, vol. 2018, pages 1-9, October.
    3. Richard Bellman, 1957. "On a Dynamic Programming Approach to the Caterer Problem--I," Management Science, INFORMS, vol. 3(3), pages 270-278, April.
    4. Liu, Xikui & Ge, Yingying & Li, Yan, 2019. "Stackelberg games for model-free continuous-time stochastic systems based on adaptive dynamic programming," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
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    Cited by:

    1. Cui, Lili & Xie, Xiangpeng & Guo, Hongyan & Luo, Yanhong, 2022. "Dynamic event-triggered distributed guaranteed cost FTC scheme for nonlinear interconnected systems via ADP approach," Applied Mathematics and Computation, Elsevier, vol. 425(C).

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