Disturbed Euler-Lagrange-based neurodynamic approach for nonsmooth noncooperative game with communication delay

This paper investigates the distributed variational generalized Nash equilibrium (vGNE) seeking problem for nonsmooth noncooperative game. Specifically, a distributed vGNE-seeking neurodynamic approach (vGSNA) modeled by disturbed Euler-Lagrange (EL) system with communication delay is designed addressing two main challenges. First of all, to realize robust vGNE computation under EL system with general bounded disturbances, a novel disturbance observer is introduced into the vGSNA to enhance the capacity of disturbance rejection. Second, detailed stability analysis is conducted via the Lyapunov-Krasovskii functionals to show the convergence of the players' actions to the vGNE under general bounded time-varying delays. Finally, to testify the efficiency of the vGSNA, an electricity market game based on generator-turbine system is presented.