Abstract and Applied Analysis
Volume 7 (2002), Issue 2, Pages 61-83

Syntheses of differential games and pseudo-Riccati equations

Yuncheng You

Department of Mathematics, University of South Florida, Tampa 33620-5700, FL, USA

Received 5 November 2001

Copyright © 2002 Yuncheng You. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


For differential games of fixed duration of linear dynamical systems with nonquadratic payoff functionals, it is proved that the value and the optimal strategies as saddle point exist whenever the associated pseudo-Riccati equation has a regular solution P(t,x). Then the closed-loop optimal strategies are given by u(t)=R1BP(t,x(t)),v(t)=S1CP(t,x(t)). For differential game problems of Mayer type, the existence of a regular solution to the pseudo-Riccati equation is proved under certain assumptions and a constructive expression of that solution can be found by solving an algebraic equation with time parameter.