On Stability of Perturbed Nonlinear Switched Systems with Adaptive Reinforcement Learning

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.

A hybrid controller method with genetic algorithm optimization to measure position and angular for mobile robot motion control

“…The most difficult part of using a PID controller is to determine the appropriate gains. Reinforcement learning (RL) is becoming more significant in real control applications due to the benefits of dealing with Riccati equations and Hamilton-Jacobi-Bellman (HJB) equations, which are impossible to solve directly ( Dao et al, 2020 ; Dao and Liu 2021 ; Vu et al, 2021 ). Actor/critic structures with Neural Networks (NNs) were presented to construct iterative algorithms with sequential tuning ( He et al, 2019 ), ( Luo et al, 2019 ) to get an approximation of the best control solution ( Bhasin et al, 2013 ).…”