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Solvability and Asymptotic Behavior of Generalized Riccati equations arising in Indefinite Stochastic LQ Controls

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Date

2001

Authors

Rami, Mustapha Ait
Chen, Xi
Moore, John
Zhou, Xun

Journal Title

Journal ISSN

Volume Title

Publisher

Institute of Electrical and Electronics Engineers (IEEE Inc)

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 infinite time horizon. Examples area presented to illustrate the results established.

Description

Keywords

Keywords: Asymptotic stability; Constraint theory; Control system analysis; Control system synthesis; Costs; Linear control systems; Optimal control systems; Problem solving; Quadratic programming; Riccati equations; Constrained matrix differential Riccati equation Asymptotic analysis; Generalized Riccati equation; Indefinite stochastic linear quadratic (LQ) control; Linear matrix inequality; Solvability

Citation

URI

http://hdl.handle.net/1885/69287

Collections

ANU Research Publications

Source

IEEE Transactions on Automatic Control

Type

Journal article

Book Title

Entity type

Access Statement

License Rights

DOI

10.1109/9.911419

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