On Stability of Perturbed Nonlinear Switched Systems with Adaptive Reinforcement Learning

Phuong Nam Dao, Hong Quang Nguyen, Minh-Duc Ngo and Seon-Ju Ahn
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Phuong Nam Dao: Department of Automatic Control, Hanoi University of Science and Technology, 1 Dai Co Viet Road, Hanoi 100000, Vietnam
Hong Quang Nguyen: Department of Automation, Thai Nguyen University of Technology, 666, 3/2 Street, Tich Luong Ward, Thai Nguyen City 251750, Vietnam
Minh-Duc Ngo: Department of Automation, Thai Nguyen University of Technology, 666, 3/2 Street, Tich Luong Ward, Thai Nguyen City 251750, Vietnam
Seon-Ju Ahn: Department of Electrical Engineering, Chonnam National University, Gwangju 61186, Korea

Energies, 2020, vol. 13, issue 19, 1-19

Abstract: In this paper, a tracking control approach is developed based on an adaptive reinforcement learning algorithm with a bounded cost function for perturbed nonlinear switched systems, which represent a useful framework for modelling these converters, such as DC–DC converter, multi-level converter, etc. An optimal control method is derived for nominal systems to solve the tracking control problem, which results in solving a Hamilton–Jacobi–Bellman (HJB) equation. It is shown that the optimal controller obtained by solving the HJB equation can stabilize the perturbed nonlinear switched systems. To develop a solution to the translated HJB equation, the proposed neural networks consider the training technique obtaining the minimization of square of Bellman residual error in critic term due to the description of Hamilton function. Theoretical analysis shows that all the closed-loop system signals are uniformly ultimately bounded (UUB) and the proposed controller converges to optimal control law. The simulation results of two situations demonstrate the effectiveness of the proposed controller.

Keywords: adaptive dynamic programming (ADP); adaptive reinforcement learning (ARL); switched systems; HJB equation; uniformly ultimately bounded (UUB); Lyapunov stability theory (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2020
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