Two-Stage Asynchronous Learning for Optimal Tracking in Multiplayer Differential Games

The optimal tracking control problem for multiplayer differential game systems (MDGS) with unknown dynamics is investigated in this article. A two-stage asynchronous learning scheme is proposed to achieve Nash equilibrium solutions without requiring initial admissible control policies. In the first stage, stabilizing control policies are constructed through a homotopic-based iterative process. In the second stage, an asynchronous policy iteration (PI) method is employed, in which players sequentially update their policies using partial real-time information, contributing to improved convergence efficiency compared to synchronous approaches. The proposed scheme is further extended to a data-driven framework, relaxing the requirement of explicit system dynamic information. Convergence under stabilizability and detectability conditions is theoretically proven. Finally, two simulation examples are conducted to demonstrate the effectiveness of the proposed method in tracking a sinusoidal reference. Additionally, comparison experiments are provided to highlight the superiority of the proposed algorithm.