A primal-dual semidefinite programming approach to linear quadratic control

David D. Yao; Shuzhong Zhang; Xun Yu Zhou

doi:10.1109/9.948474

Author(s)

David D. Yao
Shuzhong Zhang
Xun Yu Zhou

Detail(s)

Original language	English
Pages (from-to)	1442-1447
Journal / Publication	IEEE Transactions on Automatic Control
Volume	46
Issue number	9
Publication status	Published - Sep 2001
Externally published	Yes

Link(s)

DOI	DOI https://doi.org/10.1109/9.948474 Final Published version
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Link to Scopus	https://www.scopus.com/record/display.uri?eid=2-s2.0-0035441322&origin=recordpage
Permanent Link	https://scholars.cityu.edu.hk/en/publications/publication(3c361a50-9c06-44af-8735-5de00b320f9f).html

Abstract

We study a deterministic linear-quadratic (LQ) control problem over an infinite horizon, without the restriction that the control cost matrix R or the state cost matrix Q be positive-definite. We develop a general approach to the problem based on semidefinite programming (SDP) and related duality analysis. We show that the complementary duality condition of the SDP is necessary and sufficient for the existence of an optimal LQ control under a certain stability condition (which is satisfied automatically when Q is positive-definite). When the complementary duality does hold, an optimal state feedback control is constructed explicitly in terms of the solution to the primal SDP.

Research Area(s)

Complementary duality, Generalized Riccati equation, LQ control, Semidefinite programming

Citation Format(s)

[ RIS ] [ BibTeX ]

A primal-dual semidefinite programming approach to linear quadratic control. / Yao, David D.; Zhang, Shuzhong; Zhou, Xun Yu.

In: IEEE Transactions on Automatic Control, Vol. 46, No. 9, 09.2001, p. 1442-1447.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review

Yao, DD, Zhang, S & Zhou, XY 2001, 'A primal-dual semidefinite programming approach to linear quadratic control', IEEE Transactions on Automatic Control, vol. 46, no. 9, pp. 1442-1447. https://doi.org/10.1109/9.948474

Yao, D. D., Zhang, S., & Zhou, X. Y. (2001). A primal-dual semidefinite programming approach to linear quadratic control. IEEE Transactions on Automatic Control, 46(9), 1442-1447. https://doi.org/10.1109/9.948474

Yao DD, Zhang S, Zhou XY. A primal-dual semidefinite programming approach to linear quadratic control. IEEE Transactions on Automatic Control. 2001 Sep;46(9):1442-1447. https://doi.org/10.1109/9.948474

Yao, David D. ; Zhang, Shuzhong ; Zhou, Xun Yu. / A primal-dual semidefinite programming approach to linear quadratic control. In: IEEE Transactions on Automatic Control. 2001 ; Vol. 46, No. 9. pp. 1442-1447.