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