Solvability and asymptotic behavior of generalized Riccati equations arising in indefinite stochastic LQ controls

Author

Rami, Mustapha Ait ; Chen, Xi ; Moore, John B. ; Zhou, Xun Yu

Author_Institution

Dept. of Syst. Eng. & Eng. Manage., Chinese Univ. of Hong Kong, Shatin, China

Volume

46

Issue

3

fYear

2001

fDate

3/1/2001 12:00:00 AM

Firstpage

428

Lastpage

440

Abstract

The optimal control problem in a finite time horizon with an indefinite quadratic cost function for a linear system subject to multiplicative noise on both the state and control can be solved via a constrained matrix differential Riccati equation. In this paper, we provide general necessary and sufficient conditions for the solvability of this generalized differential Riccati equation. Furthermore, its asymptotic behavior is investigated along with its connection to the generalized algebraic Riccati equation associated with the linear quadratic control problem in finite time horizon. Examples are presented to illustrate the results established

Keywords

Riccati equations; differential equations; linear quadratic control; matrix algebra; noise; stochastic systems; asymptotic behavior; constrained matrix differential Riccati equation; finite time horizon; generalized differential Riccati equation; indefinite quadratic cost function; indefinite stochastic LQ controls; linear system; multiplicative noise; necessary and sufficient conditions; optimal control; solvability; Control systems; Cost function; Differential equations; Linear systems; Nonlinear equations; Optimal control; Riccati equations; Stochastic processes; Stochastic resonance; Stochastic systems;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.911419

Filename

911419