Data-driven adaptive optimal control for discrete-time periodic systems

In this paper, a problem of data-driven optimal control is studied for discrete-time periodic systems with unknown system matrices and input matrices. For this problem, a value iteration-based adaptive dynamic programming algorithm is proposed to obtain the suboptimal controller. The core of the algorithm proposed in this paper is to obtain an approximation of the unique positive definite solution of the algebraic Riccati equation and the optimal feedback gain matrix by using the collected real-time data of the system states and control inputs. Without an initial stabilizing feedback gain, the proposed algorithm could be activated by an arbitrary bounded control input. Finally, the effectiveness of the proposed approach is demonstrated by two examples.