Iteratively Computation the Nash Equilibrium Points in the Two-Player Positive Games

Abstract: We consider the linear quadratic differential games for positive linear systems with the feedback information structure and two players. The accelerated Newton method to obtain the stabilizing solution of a corresponding set of Riccati equations is presented in [6], where the convergence properties are established. In addition, the Lyapunov iterative method to compute the Nash equilibrium point is presented in [7] (5th International Conference Applied and Computational Mathematics, WSEAS Conference at Mallorca, 2016). Based on these two methods we derive a new one - the accelerated Lyapunov method. Moreover, the convergence properties are proved. The performances of the proposed algorithm are illustrated on some numerical examples.