Computational aspects of the open-loop Nash equilibrium in linear quadratic games

In this paper we consider open-loop Nash equilibria of the linear-quadratic differential game. In Engwerda (1998), both necessary and sufficient conditions for the existence of a solution for as well the finite-planning horizon case as well the infinite-planning horizon case were presented. Here we will consider computational aspects of this problem. In particular, we consider convergence aspects of the finite-planning horizon solution if the planning horizon expands. An algorithm is presented to calculate all equilibria of the infinite-planning horizon case. Furthermore, sufficient conditions on the system parameters are presented, which guarantee the existence of a unique solution for both the finite as the infinite horizon problem. (C) 1998 Elsevier Science B.V. All rights reserved.