Reinforcement Learning-Based Optimal Control for Multiplicative-Noise Systems with Input Delay

Hongxia Wang; Fuyu Zhao; Zhaorong Zhang; Juanjuan Xu; Xun Li

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arXiv · 2301.02812

Reinforcement Learning-Based Optimal Control for Multiplicative-Noise Systems with Input Delay

Hongxia Wang·Fuyu Zhao·Zhaorong Zhang·Juanjuan Xu·Xun Li

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Abstract

In this paper, the reinforcement learning (RL)-based optimal control problem is studied for multiplicative-noise systems, where input delay is involved and partial system dynamics is unknown. To solve a variant of Riccati-ZXL equations, which is a counterpart of standard Riccati equation and determines the optimal controller, we first develop a necessary and sufficient stabilizing condition in form of several Lyapunov-type equations, a parallelism of the classical Lyapunov theory. Based on the condition, we provide an offline and convergent algorithm for the variant of Riccati-ZXL equations. According to the convergent algorithm, we propose a RL-based optimal control design approach for solving linear quadratic regulation problem with partially unknown system dynamics. Finally, a numerical example is used to evaluate the proposed algorithm.

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BibTeX RIS

Hongxia Wang, Fuyu Zhao, Zhaorong Zhang, Juanjuan Xu, Xun Li. 2023-01-07. Reinforcement Learning-Based Optimal Control for Multiplicative-Noise Systems with Input Delay. https://arxiv.org/abs/2301.02812

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