Adaptive Optimal Output Regulation of Discrete-Time Linear Systems: A Reinforcement Learning Approach

In this paper, we solve the optimal output regulation problem for discrete-time systems without precise knowledge of the system model. Drawing inspiration from reinforcement learning and adaptive dynamic programming, a data-driven solution is developed that enables asymptotic tracking and disturbance rejection. Notably, it is discovered that the proposed approach for discrete-time output regulation differs from the continuous-time approach in terms of the persistent excitation condition required for policy iteration to be unique and convergent. To address this issue, a new persistent excitation condition is introduced to ensure both uniqueness and convergence of the data-driven policy iteration. The efficacy of the proposed methodology is validated by an inverted pendulum on a cart example.