Prescribed-Time Distributed Integral Sliding-Mode-Based Least-Norm Nash Equilibrium Seeking in Monotone Games Under Disturbances

This article focuses on prescribed-time distributed robust Nash equilibrium seeking for monotone games impacted by unknown and time-varying disturbances. First, a regularization term with a prescribed-time decaying parameter is introduced to compensate for the absence of strong monotonicity in the merely monotone game. Based on the regularization technique, a new prescribed-time signum-based distributed Nash equilibrium seeking algorithm incorporating an integral sliding mode method, a leader-following consensus protocol, and a gradient algorithm is presented for monotone games with unknown but bounded disturbances. Then, to dispose of the unknown bounds of disturbances, a prescribed-time distributed adaptive integral sliding mode based Nash equilibrium seeking strategy is devised. On the basis of the proposed strategies, some sufficient conditions are obtained to guarantee that the players' actions are capable of converging to the least-norm Nash equilibrium of the monotone games in a prescribed time. In the end, numerical simulations on least-distance formation control of a network of players testify to the performance of the proposed seeking strategies.