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Volume 10 Issue 3
Mar.  2023

IEEE/CAA Journal of Automatica Sinica

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Article Navigation >  IEEE/CAA Journal of Automatica Sinica  > 2023  >  10(3): 781-791
G. Y. Zhu, X. L. Li, R. R. Sun, Y. Y. Yang, and P. Zhang, “Policy iteration for optimal control of discrete-time time-varying nonlinear systems,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 3, pp. 781–791, Mar. 2023. doi: 10.1109/JAS.2023.123096
Citation: G. Y. Zhu, X. L. Li, R. R. Sun, Y. Y. Yang, and P. Zhang, “Policy iteration for optimal control of discrete-time time-varying nonlinear systems,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 3, pp. 781–791, Mar. 2023. doi: 10.1109/JAS.2023.123096
shu

Policy Iteration for Optimal Control of Discrete-Time Time-Varying Nonlinear Systems

doi: 10.1109/JAS.2023.123096
  • 1.

    Beijing Research Center of Urban Traffic Information Sensing and Service Technologies, and also with the Key Laboratory of Transport Industry of Big Data Application Technologies for Comprehensive Transport, Beijing Jiaotong University, Beijing 100044, China

  • 2.

    Transport Planning and Research Institute, Ministry of Transport, China, Beijing 100028, China

Funds:  This work was supported in part by Fundamental Research Funds for the Central Universities (2022JBZX024) and in part by the National Natural Science Foundation of China (61872037, 61273167)
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    Abstract
  • Aimed at infinite horizon optimal control problems of discrete time-varying nonlinear systems, in this paper, a new iterative adaptive dynamic programming algorithm, which is the discrete-time time-varying policy iteration (DTTV) algorithm, is developed. The iterative control law is designed to update the iterative value function which approximates the index function of optimal performance. The admissibility of the iterative control law is analyzed. The results show that the iterative value function is non-increasingly convergent to the Bellman-equation optimal solution. To implement the algorithm, neural networks are employed and a new implementation structure is established, which avoids solving the generalized Bellman equation in each iteration. Finally, the optimal control laws for torsional pendulum and inverted pendulum systems are obtained by using the DTTV policy iteration algorithm, where the mass and pendulum bar length are permitted to be time-varying parameters. The effectiveness of the developed method is illustrated by numerical results and comparisons.

     

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    Highlights

    • A novel iterative adaptive dynamic programming method is presented for the infinite horizon optimal control problem of discrete time-varying nonlinear systems
    • The properties of the discrete-time time-varying policy iteration method, including monotonicity, convergence and optimality, are analyzed in detail
    • The critic neural network and actor neural network are introduced to implement the presented method
    • Simulation results show that the presented method can obtain the optimal control law and optimal performance index function, which verifies the correctness of the presented method

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