Prescribed-time distributed Nash equilibrium seeking for noncooperation games

This paper investigates the prescribed-time distributed Nash equilibrium seeking (DNES) problem for multi-agent noncooperation games. Based on the distributed motion-planning method and the gradient search, a class of prescribed-time DNES algorithms are developed for first and second-order multi-agent systems, respectively. They may ensure each player’ s action converges to the Nash equilibrium (NE) point at a prescribed settling time in advance. Further, for the case when the velocity information of each agent is not available, an observer-based prescribed-time DNES algorithm is extended. Compared with existing works, the convergence time of proposed prescribed-time DNES algorithms in this paper can be assigned in advance by users according to task requirements. Besides, the designed DNES algorithms are sampled without continuous measurements, which means players can update their actions at each sampling moment to avoid the increasing cost brought by continuous information interaction among players. Finally, the effectiveness of algorithms proposed in this paper is verified by some numerical simulations.