Distributed Nash Equilibrium Seeking for Uncertain Euler-Lagrange Systems over Jointly Strongly Connected Networks

In this paper, we first construct a control law to solve the distributed Nash equilibrium (NE) seeking problem for games with multiple players whose actions are governed by a class of uncertain Euler-Lagrange (EL) systems. Then, we further consider the same problem with the Euler-Lagrange systems subject to trigonometric polynomial disturbances with arbitrarily unknown amplitudes, initial phases and frequencies. We integrate the internal model principle and the adaptive control technique to deal with such disturbances. Moreover, we consider jointly strongly connected switching graphs, which can be disconnected at every time instant and can switch among infinitely many static weighted graphs. Three numerical examples are used to illustrate the efficacy of our method.