Distributed Nash Equilibrium Seeking for a Class of Uncertain Nonlinear Systems Subject to Bounded Disturbances

In this article, we study the problem of the distributed Nash equilibrium seeking of $N$-player games over jointly strongly connected switching networks. The action of each player is governed by a class of uncertain nonlinear systems. Our approach integrates the consensus algorithm, the distributed estimator over jointly strongly connected switching networks, and some adaptive control techniques. Furthermore, we also consider the disturbance rejection problem for bounded disturbances with unknown bounds. A special case of our results gives the solution of the distributed Nash equilibrium seeking for high-order integrator systems.