Multiplayer Pursuit-Evasion Games With Distributed Nash Equilibrium Solution
Wenqi Xu, Tong Wang, Jianbin Qiu, Xiaoping Liu
Abstract
This paper concentrates on solving the multiplayer pursuit-evasion (MPE) game issue. In the existing MPE game framework, the fact that the Nash equilibrium and distribution are two contradicting properties which can not be achieved simultaneously. To tackle this challenge, novel cost functions that combine the best response approach and min-max scheme, are introduced such that the coupling terms in the existing MPE game formulations are removed. Consequently, the corresponding Nash and distributed solutions are obtained. Furthermore, a more general situation that the pursuers are not aware of the global information of the communication topology is discussed. In this framework, the adaptive coupling gains are incorporated into the improved cost functions to further realize the Nash equilibrium and distributed control strategies without the necessity of the information of topology graph. The sufficient conditions in two scenarios are given while the stability of adaptive coupling gains are provided as well. Besides, the Nash equilibrium properties of the solutions in two scenarios are analyzed, respectively. Finally, a simulation example is displayed to validate the theoretical results.