Learning-based Prescribed Rate Design for Output Regulation of Discrete-time Systems

This paper presents data-driven output regulation designs for unknown discrete-time systems with the prescribed convergence rate. After integrating the convergence rate specified by the designer, the tracking problem is composed of learning two components: a feedback control gain and solutions to output regulator equations. The RL algorithm can learn the feedback control gain from system measurements from a specified auxiliary system without knowing its full dynamics. Then output regulator equations associated with the convergence rate are solved as a feedforward control gain by leveraging the system data rather than the dynamic model. The proposed designs assure that the tracking error asymptotically converges to zero at the prescribed convergence rate. The simulation results show the effectiveness of the proposed methods.