Bias-policy iteration based optimal control for unknown continuous-time linear periodic systems

In this paper, the optimal control problem for unknown continuous-time linear periodic (CTLP) systems is investigated. A model-based bias-policy iteration algorithm for CTLP systems with its convergence proof is established firstly. Based on that, the data-driven implementation is proposed to approximate the optimal controller without the knowledge of system dynamics. Compared with the existing methods, the advantages of the proposed method are that, the initial stabilizing controller requirement is relaxed, and the approximate optimal controller can be obtained without solving nonlinear differential equations. The numerical simulation verifies the effectiveness of the proposed method.