Hierarchical Predefined-Time NE Seeking for Uncertain Multiplayer Noncooperative Games

In this brief, we investigate the predefined-time Nash equilibrium (NE) seeking problem for the uncertain noncooperative games with second-order nonlinear dynamics. The cost function of each player is affected by the uncertain factors. In order to reduce the computational cost and achieve rapid convergence, we propose a novel time base generator (TBG) and a hierarchical predefined-time NE seeking (HPNES) algorithm by using the observer, the gradient method and the sliding mode control method. Based on the theories of symbolic-graphic combination, convex optimization and Lyapunov criteria, the sufficient conditions of the control gains are presented to guarantee the seeking of the NE. Finally, the effectiveness of the proposed algorithms is verified through the simulations.