Robust Control of Uncertain Linear Systems Based on Reinforcement Learning Principles

In this paper, a reinforcement learning (RL) approach is developed to solve the robust control for uncertain continuous-time linear systems. The objective is to find a feedback control law for the uncertain linear system using an online policy iteration algorithm. The robust control problem is solved by constructing an extended algebraic Riccati equation with properly defined weighting matrices for a general uncertain linear system. An online policy iteration algorithm is developed to solve the robust control problem based on RL principles without knowing the nominal system matrix. The convergence of the algorithm to the robust control solution for uncertain linear systems is proved. The simulation examples are given to demonstrate the effectiveness of the proposed algorithm. The results extend the design method of robust control to uncertain linear systems.