Pre-specified-time Distributed Nash Equilibrium Seeking for Games

This paper considers the Nash equilibrium seeking problem of the game in the multi-agent system. Different from the existing research, a new method is proposed by multi-step planning to solve the pre-specified-time game, which based on the technique of the leader-following consensus protocol and gradient play. The algorithm, which players can update their action at each sampling moment, is designed to enable each player's behavior converge to the Nash equilibrium point of the game at a specified time that can be appointed in advance. In addition, the players communicate via an undirected and connected network. Finally, the algorithm proposed in this paper is verified by numerical simulations.