Digital Object Identifier (DOI)
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)=−R−1B∗P(t,x(t)), v(t)=−S−1C∗P(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.
This work is licensed under a Creative Commons Attribution 3.0 License.
Was this content written or created while at USF?
Citation / Publisher Attribution
Abstract and Applied Analysis, v. 7, art. 319386
Scholar Commons Citation
You, Yuncheng, "Syntheses of Differential Games and Pseudo-Riccati Equations" (2002). Mathematics and Statistics Faculty Publications. 71.