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Solving optimal predictor-feedback control using approximate dynamic programming
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DOI：10.1016/j.automatica.2024.111848.png)
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This paper is concerned with approximately solving the optimal predictor-feedback control problem of multiplicative-noise systems with input delay in infinite horizon. The optimal predictor-feedback control, provided by the analytical method, is determined by Riccati-ZXL equations and is hard to obtain in the case of unknown system dynamics. We aim to propose a policy iteration (PI) algorithm for solving the optimal solution by approximate dynamic programming. For convergence analysis of the algorithm, we first develop a necessary and sufficient stabilizing condition, in the form of several new Lyapunov-type equations, which parameterizes all predictor-feedback controllers and can be seen as an important addition to Lyapunov stability theory. We then propose an iterative scheme for the Riccati-ZXL equations computations, along with convergence analysis, based on the condition. Inspired by this scheme, a data-driven online PI algorithm, convergence implied in that of the iterative scheme, is proposed for the optimal predictor-feedback control problem without full system dynamics. Finally, a numerical example is used to evaluate the proposed PI algorithm. (c) 2024 Published by Elsevier Ltd.
Keyword:
Stochastic system
Optimal control
Input delay
Approximate dynamic programming
期刊
IF:
5.9
论文数:
1.2W
被引数:
5.2W
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