A distributed algorithm for aggregative games of disturbed Euler-Lagrange systems

An aggregative game of disturbed Euler-Lagrange systems is studied in this paper. The cost function of each player depends on its own decision and the aggregate of all decisions. Different from the well-known aggregative games, the second-order nonlinear dynamic of every player is considered in our problem, and every player is influenced by exogenous disturbances. To seek the Nash equilibrium, a distributed algorithm is developed via state feedback, gradient descent, and internal model. The convergence of the algorithm is analyzed with the help of variational analysis and Lyapunov stability theory. It shows that the Euler-Lagrange players with the proposed algorithm, can asymptotically converge to the Nash equilibrium, even though exogenous disturbances have impact on the behaviors of the players. Finally, a numerical simulation is given to illustrate the effectiveness of our algorithm.