Reinforcement learning for adaptive optimal control of continuous-time linear periodic systems

This paper studies the infinite-horizon adaptive optimal control of continuous-time linear periodic (CTLP) systems, using reinforcement learning techniques. By means of policy iteration (PI) for CTLP systems, both on-policy and off-policy adaptive dynamic programming (ADP) algorithms are derived, such that the solution of the optimal control problem can be found without the exact knowledge of the system dynamics. Starting with initial stabilizing controllers, the proposed PI-based ADP algorithms converge to the optimal solutions under mild conditions. Application to the adaptive optimal control of the lossy Mathieu equation demonstrates the efficacy of the proposed learning-based adaptive optimal control algorithm.