Distributed Nash Equilibrium Seeking of Networked Nonlinear Systems over Directed Graphs

In this paper, the distributed Nash equilibrium seeking problem of aggregative games, with players been presented by uncertain nonlinear systems over directed graphs, is investigated. The problem aims at designing a distributed algorithm for each player such that the player's state is bounded, while the player's output converges to the Nash equilibrium point. A dynamic compensator is firstly proposed by utilizing gradient-based protocol and average consensus strategy. Then the distributed Nash equilibrium seeking problem is converted into a tracking problem. Finally, the resulting tracking problem is addressed by developing a novel output feedback controller. It is shown that the concerned distributed Nash equilibrium seeking problem can be solved by the distributed algorithm composed of the dynamic compensator and the output feedback controller.