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.