Zero-sum Game Optimized Control With Augmented Time-synchronized Property

This paper proposes and rigorously develops a reinforcement learning(RL)-based optimized control strategy with notable time-synchronized stability (TSS) properties for zero-sum differential games. The proposed method addresses the challenge of approximating the time-synchronized Nash equilibrium solutions in nonlinear systems governed by the Hamilton-Jacobi-Isaacs (HJI) equation. By incorporating a norm-normalized sign function into the learning framework, the system ensures all state-variables converge simultaneously, improving robustness and energy efficiency. The RL-based optimization iteratively refines the control policies while maintaining system stability underpinned rigorously by Lyapunov-based analysis. To demonstrate the effectiveness of the proposed approach, a motion control problem for an autonomous vehicle system is simulated; comparing the results with alternative existing fixed-time sliding control (FTC) and time-synchronized optimized control methods. The results illustrate that the proposed control strategy enhances convergence speed, smoothness, and disturbance rejection, making it well-suited for the requirements of real-world high-precision control applications.