Reduced-order online robust control for linear systems over stochastic MIMO vehicular channels

Ensuring robust control in uncertain dynamic systems over wireless networks is increasingly vital for applications such as autonomous vehicles and industrial automation. Traditional robust control methods often fall short in real-time wireless settings due to computational overhead and oversimplified channel models. This work introduces a novel online control framework tailored for linear systems operating over stochastic MIMO fading channels with model uncertainties. By transforming the original robust control task into a reduced-order ergodic optimal control problem, the proposed method enables efficient policy learning while avoiding the curse of dimensionality in traditional Bellman equation approaches. To establish theoretical guarantees, the paper employs a controllability cone decomposition technique together with Lyapunov analysis to derive necessary and sufficient conditions for the existence of the optimal solution to the virtual optimal control problem, as well as sufficient conditions for the robust stability of the closed-loop system. Leveraging stochastic approximation (SA) and Lyapunov-based ordinary differential equation (ODE) analysis, we propose an efficient online algorithm that provably converges to the optimal policy. Simulation results confirm that the proposed approach achieves superior stability, convergence, and computational performance compared to existing baselines. This work provides a scalable and theoretically grounded solution for real-time robust control in dynamic and uncertain wireless environments.