Sliding mode extremum seeking control for linear quadratic dynamic game

The extremum seeking control has been proposed to find a set point and/or track a time-varying set point so that a performance index of the system reaches its extremum point. In this paper, the extremum seeking control with sliding mode is extended to solve the Nash equilibrium solution for an n-person linear quadratic dynamic game. For each player, a sliding mode extremum seeking controller is designed to let the player´s linear quadratic performance index track a decreasing signal so that the Nash equilibrium point is reached.