Data-Driven Control Algorithms for Unknown Discrete-Time Linear Periodic Systems

In this article, the data-driven optimal control problem is addressed for discrete-time linear periodic systems with unknown system dynamics. To reduce the number of iterations required by existing data-driven control algorithms, two novel value iteration (VI)-based adaptive dynamic programming (ADP) algorithms are presented. In these two VI algorithms, the latest updated estimates are utilized to approximate the unique positive definite solution of the algebraic Riccati matrix equation (ARE), and the suboptimal controller is obtained. Since the latest estimation is generally closer to the optimal value than that of the last iteration step, the number of iterations is significantly reduced in the two proposed algorithms. Moreover, the backward VI algorithm requires fewer iteration steps compared to the forward VI algorithm. In addition, the proposed methods do not require an initial stabilizing controller. Finally, two examples are provided to demonstrate the effectiveness of the two proposed iterative algorithms.