Neural Network-based Distributed Generalized Nash Equilibrium Seeking for Uncertain Nonlinear Multi-agent Systems

This paper investigates distributed variational generalized Nash equilibrium (v-GNE) seeking problems in heterogeneous high-order nonlinear multi-agent systems with partially unknown dynamics. To overcome the difficulties brought by high-order uncertain physical dynamics, we introduce a virtual decision with a primal-dual update for each player and design reference-tracking schemes to guide the players' outputs toward the v-GNE. Besides, we incorporate a shallow neural network (NN)-based dynamic estimator to handle the unknown nonlinear dynamics. Through Lyapunov analysis, we demonstrate that the players' behaviors converge to the v-GNE with an arbitrarily small error. Numerical simulations of connectivity control games and energy consumption games illustrate the effectiveness of our algorithm.