Online Learning Algorithms for Zero-Sum Games of Linear Systems over Wireless MIMO Fading Channels with Uncountable State Space
Minjie Tang, Vincent K. N. Lau · 2023
In this paper, we consider an online learning framework for a zero-sum game of an unstable linear dynamic system in the presence of wireless MIMO fading channels between the remote controllers and the actuator of the dynamic plant. We first formulate the stochastic zero-sum game as ergodic optimization problems, and propose a pair of equiv-alent reduced-state Bellman optimality equations to address the “curse of dimensionality” for Nash equilibrium of the game. Based on the reduced-state Bellman optimality equations, we analyze the structural properties of the Nash equilib-rium and propose a novel low-complexity online stochastic-approximation(SA)-based algorithm to solve the reduced-state Bellman optimality equations. Numerical results are analyzed for the proposed learning scheme and several state-of-the-art learning approaches in terms of the computational complexity, the convergence performance as well as the robustness per-formance. We show that a significant performance gain can be achieved by the proposed scheme compared to the baseline approaches.