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14 March 2002 Syntheses of differential games and pseudo-Riccati equations
Yuncheng You
Abstr. Appl. Anal. 7(2): 61-83 (14 March 2002). DOI: 10.1155/S1085337502000817

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)=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.

Citation

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Yuncheng You. "Syntheses of differential games and pseudo-Riccati equations." Abstr. Appl. Anal. 7 (2) 61 - 83, 14 March 2002. https://doi.org/10.1155/S1085337502000817

Information

Published: 14 March 2002
First available in Project Euclid: 14 April 2003

zbMATH: 1066.91013
MathSciNet: MR1891031
Digital Object Identifier: 10.1155/S1085337502000817

Subjects:
Primary: 47J25, 49J35
Secondary: 49N70, 91A23

Rights: Copyright © 2002 Hindawi

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Vol.7 • No. 2 • 14 March 2002
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