Reinforcement learning and non-zero-sum game output regulation for multi-player linear uncertain systems

Abstract

This paper studies the non-zero-sum game output regulation problem (GORP) for a class of continuous-time multi-player linear systems. Without the knowledge of state and input matrices, the Nash equilibrium solution, N-tuple of feedback control policy, is learned through online data collected along the system trajectories. A key strategy is, for the first time, to combine techniques from reinforcement learning (RL), differential game theory, and output regulation for data-driven control design. Different from the existing literature of adaptive optimal output regulation, the feedforward matrices are considered nontrivial. Theoretical analysis shows the disturbance rejection and tracking ability of the closed-loop system. Simulation results demonstrate the efficacy of the developed data-driven control approach.