Reinforcement Learning for H ∞ Optimal Control of Unknown Continuous-Time Linear Systems
针对未知动态的连续时间线性系统，提出基于初始激励的强化学习算法，在可在线验证的初始激励条件下学习H∞最优控制策略，避免持续激励条件或数据存储机制。
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.