Linear Quadratic Nash Games on Positive Linear Systems

Abstract

In this paper two-player Nash differential games, on an infinite time horizon, with two different information structures have been considered: the open loop and the deterministic feedback information structure. The performance indices were assumed to be of quadratic type and the constraint to be a linear positive differential system. As the main result, a convergent Newtonian algorithm to solve the associated algebraic matrix Riccati equation and generalized algebraic matrix Riccati equation in order to obtain stabilizing solutions which are directly related to the existence of a Nash equilibrium, is presented for each information structure. Finally, we discuss a numerical example to illustrate both algorithms presented.