Game-Theoretic Approaches for Robust Stability of DC Motor Systems

This study proposes a game-theoretic framework for achieving robust stability in DC motor systems operating under parametric uncertainty and external disturbances. We model the controller, disturbance, and uncertainty as strategic players in a non-cooperative differential game and synthesize equilibrium policies using a Lyapunov–game approach. Practically, the method integrates: 1) LMI-based stabilization to certify descent conditions, 2) actor–critic reinforcement learning to approximate the Hamilton–Jacobi–Isaacs (HJI) value function beyond linear regimes, and 3) evolutionary/swarm optimization for controller initialization and distributed observer tuning. We validate the framework on a separately excited DC motor subject to ±20% parameter variations and a bounded load-torque disturbance and compare it against PID and H8 baselines. Simulations show consistently faster rise/settling, lower overshoot, stronger disturbance rejection at a step disturbance, and smoother control effort, while attaining the highest qualitative robustness margin among the tested controllers. Beyond single-motor stabilization, we outline extensions to multi-agent coordination, security-aware control, and fractional/fuzzy models, demonstrating adaptability and scalability of the approach. These results indicate that framing stability as the outcome of strategic interactions yields reliable and efficient DC-motor control in uncertain, adversarial environments.