A Novel Second-Order Neurodynamic System to Fixed-Time Nash Equilibrium Seeking

In this paper, we investigate fixed-time (FT) Nash equilibrium (NE) seeking problem for non-cooperative games. A novel second-order NE seeking neurodynamic system is proposed to accelerate the convergence. The proposed neurodynamic system's trajectory converges to NE within fixed-time under potential function and strongly monotone potential function respectively. It is shown that the upper bounds of the settling time are independent of the initial state of the system. The robustness of the proposed NE seeking neurodynamic system under bounded perturbations is further studied. The practicability of the proposed NE seeking system is illustrated via a simulation example and an analog circuit implementation on Multisim 14.3.