H-Infinity Tracking for Intelligent Edge-Controlled Systems over Fading Channels in AI-RAN

In this work, we study the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> tracking control problem for a linear system over random wireless multiple-input multiple-output (MIMO) fading channels between the remote tracking controller and the dynamic plant. We first formulate the problem as a stochastic zero-sum game and derive the corresponding coupled optimality condition that characterizes the Nash equilibrium. To mitigate the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">curse of dimensionality</i>, we introduce an equivalent structured reduced-order optimality condition which significantly simplifying the problem. Leveraging this framework, we propose an online learning algorithm that utilizes structured stochastic approximation (SA) to asymptotically learn the Nash equilibrium in real time. Through extensive numerical simulations, we validate the effectiveness of our approach, demonstrating its superior tracking accuracy, convergence speed, and computational efficiency compared to state-of-the-art methods.