A primal-dual semi-definite programming approach to linear quadratic control

Author

Yao, David D. ; Zhang, Shuzhong ; Zhou, Xun Yu

Author_Institution

Dept. of Ind. Eng. & Oper. Res., Columbia Univ., New York, NY, USA

Volume

46

Issue

9

fYear

2001

fDate

9/1/2001 12:00:00 AM

Firstpage

1442

Lastpage

1447

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 semi-definite 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

Keywords

Riccati equations; duality (mathematics); linear quadratic control; mathematical programming; matrix algebra; stability; state feedback; Riccati equation; complementary duality; control cost matrix; linear quadratic control; optimal control; semidefinite programming; stability; state cost matrix; state feedback; Automatic control; Costs; Infinite horizon; Linear programming; Optimal control; Quadratic programming; Research and development management; Riccati equations; Symmetric matrices; Systems engineering and theory;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.948474

Filename

948474