Nash solution by extremum seeking control approach

In this paper, we propose an algorithm to solve the Nash equilibrium solution for an n-person noncooperative dynamic game by the extremum seeking control approach with sliding mode. For each player, a switching function is defined as the difference between the player´s cost function and a reference signal. The extremum seeking controller for each player is designed so that the system converges to a sliding boundary layer defined in the vicinity of a sliding mode corresponding to the switching function and inside the boundary layer, the cost function tracks the reference signal and converges it to the Nash equilibrium solution.