Data-Driven Adaptive Control for Discrete-Time Linear Systems With Delayed Inputs

In this article, the stabilization problem is investigated for input-delayed systems with unknown system dynamics. To solve this problem, a value iteration (VI)-based adaptive dynamic programming (ADP) algorithm is established to learn the state feedback controller from the data along the trajectory of the system. In order to design this control algorithm, the input-delayed system is transformed into a delay-free system at first. Thus, the algebraic Riccati matrix equation (ARE) of the delay-free system is iteratively solved in the absence of system model, and then the controller is designed by using the approximation to the solution of the ARE. In particular, the rank condition of the data-constructed matrices is satisfied by utilizing basis functions, and an initial stabilizing controller is not required in the proposed algorithm. Finally, the effectiveness of the proposed algorithm is illustrated by two practical examples.