Robust Output Regulation and Reinforcement Learning-based Output Tracking Design for Unknown Linear Discrete-Time Systems

TL;DR

This paper develops a reinforcement learning-based method for optimal output tracking in unknown linear discrete-time systems, combining robust output regulation theory with data-driven control to achieve accurate tracking without full system knowledge.

Contribution

It introduces an off-policy RL algorithm that uses only output data to solve the output regulation problem, removing the need for complete system dynamics knowledge.

Findings

Proposes a novel RL algorithm for output tracking with unknown systems.

Ensures the uniqueness of the control solution via rank condition analysis.

Demonstrates effective output tracking using only measured output data.

Abstract

In this paper, we investigate the optimal output tracking problem for linear discrete-time systems with unknown dynamics using reinforcement learning and robust output regulation theory. This output tracking problem only allows to utilize the outputs of the reference system and the controlled system, rather than their states, and differs from most existing tracking results that depend on the state of the system. The optimal tracking problem is formulated into a linear quadratic regulation problem by proposing a family of dynamic discrete-time controllers. Then, it is shown that solving the output tracking problem is equivalent to solving output regulation equations, whose solution, however, requires the knowledge of the complete and accurate system dynamics. To remove such a requirement, an off-policy reinforcement learning algorithm is proposed using only the measured output data along the trajectories of the system and the reference output. By introducing re-expression error and analyzing the rank condition of the parameterization matrix, we ensure the uniqueness of the proposed RL based optimal control via output feedback.