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

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

Description

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...[Show more]

dc.contributor.authorRami, Mustapha Ait
dc.contributor.authorChen, Xi
dc.contributor.authorMoore, John
dc.contributor.authorZhou, Xun
dc.date.accessioned2015-12-10T23:33:23Z
dc.date.available2015-12-10T23:33:23Z
dc.identifier.issn0018-9286
dc.identifier.urihttp://hdl.handle.net/1885/69287
dc.description.abstractThe 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.
dc.publisherInstitute of Electrical and Electronics Engineers (IEEE Inc)
dc.sourceIEEE Transactions on Automatic Control
dc.subjectKeywords: 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
dc.titleSolvability and Asymptotic Behavior of Generalized Riccati equations arising in Indefinite Stochastic LQ Controls
dc.typeJournal article
local.description.notesImported from ARIES
local.description.refereedYes
local.identifier.citationvolume46
dc.date.issued2001
local.identifier.absfor010203 - Calculus of Variations, Systems Theory and Control Theory
local.identifier.ariespublicationMigratedxPub1979
local.type.statusPublished Version
local.contributor.affiliationRami, Mustapha Ait, Chinese University of Hong Kong
local.contributor.affiliationChen, Xi, Chinese University of Hong Kong
local.contributor.affiliationMoore, John, College of Engineering and Computer Science, ANU
local.contributor.affiliationZhou, Xun, University of Washington
local.bibliographicCitation.issue3
local.bibliographicCitation.startpage428
local.bibliographicCitation.lastpage440
local.identifier.doi10.1109/9.911419
dc.date.updated2015-12-10T11:28:08Z
local.identifier.scopusID2-s2.0-0035278756
CollectionsANU Research Publications

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