Neurodynamic Optimization Approaches with Fixed-Time Convergence for Nash Equilibrium Seeking: Theory and Hardware Experiment

The convergence rate is one of the key performance measures for Nash equilibrium (NE) seeking strategies. In this work, we present several novel fast decoupled/coupled time-varying neurodynamic optimization approaches with fixed-time (FT) convergence to Nash equilibrium seeking in non-cooperative games. The dynamics trajectories are demonstrated to converge to the NE solution within a fixed time from any initial states. The proposed neurodynamic networks exhibit a faster convergence rate with appropriately selected time-varying coefficients. Additionally, the upper bounds of the convergence time of the proposed NE seeking networks are smaller than those for strategies with constant coefficients. The robustness of the proposed NE seeking neurodynamic approaches under bounded perturbations is further studied. The efficacy and practicality of the proposed NE seeking approaches are validated through simulations and field-programmable gate array (FPGA) experiments on duopoly market games.