Zero-sum game-based dynamic self-triggered sliding mode control for unknown nonlinear systems with asymmetric input...

This article addresses a zero-sum game-based dynamic self-triggered sliding mode control problem for continuous-time unknown nonlinear systems with asymmetric input constraints using the adaptive dynamic programming method. First, a novel nonquadratic value function incorporating sliding mode variables is formulated to systematically convert the H_∞ constrained control problem into an unconstrained zero-sum game problem. A data-driven method employing recurrent neural networks subsequently reconstructs the unknown system dynamics. Building upon this foundation, a novel dynamic self-triggered mechanism is designed, where triggering instants are adaptively determined through predictive computation involving current state information and time-decaying dynamic thresholds. To resolve the derived Hamilton-Jacobi-Isaacs equation, a streamlined single-critic neural architecture is proposed, eliminating the conventional actor-network dependency while preserving approximation accuracy. Through rigorous Lyapunov-based analysis, all closed-loop signals are theoretically guaranteed to achieve uniform ultimate boundedness. The designed control strategy is conclusively validated through comprehensive simulation studies implemented on a robotic arm system and a microgrid system, demonstrating excellent dynamic response characteristics.