Stochastic linear-quadratic control via semidefinite programming

Citation
Dd. Yao et al., Stochastic linear-quadratic control via semidefinite programming, SIAM J CON, 40(3), 2001, pp. 801-823
Citations number
26
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Mathematics,"Engineering Mathematics
Journal title
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
ISSN journal
0363-0129 → ACNP
Volume
40
Issue
3
Year of publication
2001
Pages
801 - 823
Database
ISI
SICI code
0363-0129(20011119)40:3<801:SLCVSP>2.0.ZU;2-Z
Abstract
We study stochastic linear-quadratic (LQ) optimal control problems over an infinite time horizon, allowing the cost matrices to be indefinite. We deve lop a systematic approach based on semidefinite programming (SDP). A centra l issue is the stability of the feedback control; and we show this can be e ffectively examined through the complementary duality of the SDP. Furthermo re, we establish several implication relations among the SDP complementary duality, the ( generalized) Riccati equation, and the optimality of the LQ control problem. Based on these relations, we propose a numerical procedure that provides a thorough treatment of the LQ control problem via primal-du al SDP: it identifies a stabilizing feedback control that is optimal or det ermines that the problem possesses no optimal solution. For the latter case , we develop an epsilon -approximation scheme that is asymptotically optima l.