Reinforcement-Learning Robust Tracking Control of Discrete-Time Systems with Diagonal Scaling

Abstract

This paper addresses a robust tracking problem for linear discrete-time systems by proposing a reinforcement learning (RL) control method based on a diagonal-scaling strategy, offering a solution tailored to the demands of enhanced reliability. To overcome a common limitation in policy-iteration-based RL design, namely, the reliance on an initially stabilizing solution, the tracking control problem is reformulated within the robust output regulation framework as a data-driven, solvable form. A convergence-rate condition is incorporated to relax the dependence on an initial stable control policy. The core contribution lies in addressing unknown system dynamics through a diagonal-scaling strategy, as opposed to conventional scalar convergence-rate scaling. The proposed method enables more flexible and precise closed-loop pole placement. The resulting data-driven controller guarantees asymptotic convergence of the tracking error to zero while maintaining robustness against dynamic uncertainties, ensuring computational efficiency and practical ease of implementation.