Reinforcement Learning for <i>H</i> ∞ Optimal Control of Unknown Continuous-Time Linear Systems

Designing the optimal control for the practical systems is challenging due to the unknown system dynamics and unavoidable external disturbances. In this article, the $H_{\infty } $ optimal control problem is investigated for continuous-time linear systems with unknown dynamics. The existing reinforcement learning-based $H_{\infty } $ optimal control methods require persistence of excitation (PE) condition or data storage mechanism to guarantee the convergence of the algorithms. However, PE condition is hard to be monitored online and data storage mechanism requires to store huge amounts of past system data. In order to solve these problems, the initial excitation-based reinforcement learning algorithms are presented to learn the optimal control policy under an online-verifiable initial excitation condition. The properties of the initial excitation-based reinforcement learning algorithms are analyzed, which show that the presented algorithms converge to the optimum under the initial excitation condition. Numerical analysis is provided which demonstrates the correctness of the presented algorithms.