Data-driven output regulation control for constrained linear systems

This study introduces a data-driven approach for state and output feedback control addressing the constrained output regulation problem in unknown linear discrete-time systems. Our method ensures effective tracking performance while satisfying the state and input constraints, even when system matrices are not available. We first establish a sufficient condition necessary for the existence of a solution pair to the regulator equation and propose a data-based approach to obtain the feedforward and feedback control gains for state feedback control using linear programming. Furthermore, we design a refined Luenberger observer to accurately estimate the system state, while keeping the estimation error within a predefined set. By combining output regulation theory, we develop an output feedback control strategy. The stability of the closed-loop system is rigorously proved to be asymptotically stable by further leveraging the concept of λ-contractive sets.