Distributed Nash Equilibrium Seeking for Games in Uncertain Nonlinear Systems via Adaptive Backstepping Approach

In this article, we investigate the distributed Nash equilibrium seeking for games in a class of uncertain nonlinear systems, in which players communicate with their neighbors via a strongly connected and weight-balanced digraph. First, consensus-based adaptive Nash equilibrium seeking is studied for first-order nonlinear systems with parameter uncertainties. The case of high-order systems with mismatched parameter uncertainties and nonlinearities is then considered, and a distributed adaptive Nash equilibrium seeking algorithm is designed by incorporating the celebrated adaptive backstepping technique. Under the Lyapunov stability analysis, it is proved that the players' actions can globally asymptotically converge to the Nash equilibrium by the proposed seeking strategies. Finally, simulation results show the validness of the seeking strategies.