Distributed Nash Equilibrium Seeking Algorithms for Uncertain Linear Multi-agent Systems

This paper studies the Nash equilibrium seeking problem for a group of high-order players, where each player is modeled as an uncertain linear system with a payoff function depending on all players’ output decisions. Compared with most existing Nash equilibrium seeking results, a distinctive feature of our problem is that the decision profile of each agent fails to be directly assignable and can only be changed through an uncertain high-order dynamics by selecting some admissible control inputs. We present a two-step design for distributed integral feedback controller to solve the problem via available partial information of the whole multi-agent system. The outputs of players are shown to reach the expected Nash equilibrium irrespective of the unknown parameters under the developed algorithm. The efficacy of our design is verified by a numerical example.