Neural-Network-Based Distributed Generalized Nash Equilibrium Seeking for Uncertain Nonlinear Multiagent Systems

This article investigates distributed variational generalized Nash equilibrium (v-GNE)-seeking problems in heterogeneous high-order nonlinear multiagent 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-based dynamic estimator to handle the unknown nonlinear dynamics. Through the 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.