Adaptive optimal control approach to robust tracking of uncertain linear systems based on policy iteration

Abstract

In this study, an optimal adaptive control approach is established to solve the robust output tracking problem of a class of continuous time uncertain linear systems based on the policy iteration (PI) in actor-critic algorithm. First, by augmenting the integral variables of the tracking error into state variables, the robust tracking problem is transformed into a robust control problem of an augmented uncertain linear system. It is proven that the robust control law of the augmented system enables the output of the considered system to track a polynomial time signal asymptotically. Second, an optimal control method in the corresponding auxiliary nominal system is established, and based on the Bellman optimality principle, PI algorithms are proposed to solve online tracking controllers for the matched and the mismatched uncertain systems. Finally, for testing the availability of the proposed approach and theoretical results, two numerical experiments are provided.

Robust Control of An Inverted Pendulum System Based on Policy Iteration in Reinforcement Learning

“…In the case of the linear system, system data are collected, and the solution of the HJB equation is obtained via online policy iteration (PI) using the least squares method. Xu et al [26,27] proposed an RL algorithm based on linear continuous-time systems to solve the robust control and robust tracking problems through online PI. The algorithm takes into consideration the uncertainty in the system's state and input matrices and improves the method for solving robust control.…”