## Abstract and Applied Analysis

### Syntheses of differential games and pseudo-Riccati equations

Yuncheng You

#### Abstract

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 $u(t)= -R^{-1}B^\ast P(t,x(t)),v(t)= -S^{-1}C^\ast P(t,x(t))$. 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.

#### Article information

Source
Abstr. Appl. Anal., Volume 7, Number 2 (2002), 61-83.

Dates
First available in Project Euclid: 14 April 2003

https://projecteuclid.org/euclid.aaa/1050348505

Digital Object Identifier
doi:10.1155/S1085337502000817

Mathematical Reviews number (MathSciNet)
MR1891031

Zentralblatt MATH identifier
1066.91013

#### Citation

You, Yuncheng. Syntheses of differential games and pseudo-Riccati equations. Abstr. Appl. Anal. 7 (2002), no. 2, 61--83. doi:10.1155/S1085337502000817. https://projecteuclid.org/euclid.aaa/1050348505

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