Reach-avoid differential graphical games for single evader and multiple pursuers with nonlinear dynamics

Abstract

This paper investigates the single-evader and multi-pursuer (SEMP) reach-avoid differential graphical (RADG) games of nonlinear heterogeneous players subject to saturated input and limited communication channels. The evader’s objective is to reach a designated target area while avoiding the pursuers, whose aim is to intercept the evader. First, we reformulate the SEMP RADG game as an optimal control problem within a weighted communication topology graph by incorporating the interception and control errors. Then, optimal control strategies that account for input saturation are derived by solving the coupled Hamilton-Jacobi (HJ) equations. These strategies are shown to constitute the Nash Equilibrium (NE) of the game. In addition, four types of pursuers, namely, isolated, passive, invisible, and regular pursuers, are defined based on the communication topology, and the conditions for achieving an Interactive Nash Equilibrium (INE), which is proposed for SEMP RADG games, are analyzed. Moreover, a single-network approximate dynamic programming (ADP) algorithm using concurrent learning (CL) is proposed to provide the near-optimal solutions to the coupled HJ equations. Asymptotic capture conditions are established through an examination of equilibrium points, and extensions to general pursuit-evasion (PE) games and half-space targets are further discussed. Our results are validated through numerical simulations.