Time-Varying Momentum-Like Neurodynamic Optimization Approaches With Fixed-Time Convergence for Nash Equilibrium Seeking in Noncooperative Games

Abstract

In this article, several novel time-varying momentum-like neurodynamic optimization approaches are proposed for Nash equilibrium (NE) seeking of noncooperative games. It is shown that the dynamics trajectories converge to NE within fixed-time from arbitrary initial conditions, achieving a quicker convergence rate through the selection of distinct time-varying coefficients. Moreover, the upper bounds of the settling time for the proposed NE seeking neurodynamic approaches are explicitly provided. In addition, the study investigates the robustness of the designed neurodynamic approaches in the presence of bounded noises. The superior convergence properties and practicability of our approaches are demonstrated through a simulation example involving energy consumption games.