Authors

J. R. Sun;J. M. Yong

Comments

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Abbreviated Journal Title

SIAM J. Control Optim.

Keywords

stochastic differential equation; linear quadratic differential game; two-person; zero-sum; saddle point; Riccati differential equation; closed-loop; open-loop; RICCATI-EQUATIONS; RANDOM-COEFFICIENTS; 2-PERSON; Automation & Control Systems; Mathematics, Applied

Abstract

In this paper, we consider a linear quadratic stochastic two-person zero-sum differential game. The controls for both players are allowed to appear in both drift and diffusion of the state equation. The weighting matrices in the performance functional are not assumed to be definite/nonsingular. The existence of an open-loop saddle point is characterized by the existence of an adapted solution to a linear forward-backward stochastic differential equation with constraints, together with a convexity-concavity condition, and the existence of a closed-loop saddle point is characterized by the existence of a regular solution to a Riccati differential equation. It turns out that there is a significant difference between open-loop and closed-loop saddle points. Also, it is found that there is an essential feature that prevents a linear quadratic optimal control problem from being a special case of linear quadratic two-person zero-sum differential games.

Journal Title

Siam Journal on Control and Optimization

Volume

52

Issue/Number

6

Publication Date

1-1-2014

Document Type

Article

Language

English

First Page

4082

Last Page

4121

WOS Identifier

WOS:000346845100025

ISSN

0363-0129

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