Robust Control for Multiplayer Nonzero-Sum Differential Games With Switching Topology and Input Delay

Abstract

This article investigates a multiplayer nonzero-sum differential game (MNDG) with switching topology and input delay. The Hamilton–Jacobi–Isaacs (HJI) equation is used to derive the optimal control strategies. To solve the issue of switching topology, the control strategies are decoupled with the communication topology. Then, the stability of the system can be achieved regardless of changes in communication topology with the designed control strategies. This does not require a restriction on the dwell time, making the system stability conditions more relaxed. The Lyapunov–Krasovskii functional (LKF) is constructed to prove the stability of the system in the presence of time-varying input delay. To cope with the real-world situation, the input delay is considered to be disturbed by a time-varying perturbation in this article. With these treatments, the system is more in line with real-world applications. Simulation examples are given to validate the efficiency of the presented methods.