NDLI: Indefinite Stochastic LQ Control with Markovian Jumps via Semidefinite Programming (I)

Content Provider	IEEE Xplore Digital Library
Author	Chengxin Luo Desheng Li
Copyright Year	2006
Description	Author affiliation: Sch. of Math. & Syst. Sci., Shenyang Normal Univ. (Chengxin Luo; Desheng Li)
Abstract	This paper studies a stochastic linear-quadratic (LQ) control problem over an infinite time horizon with Markovian jumps in parameter values, allowing the weighting matrices in the cost to be indefinite. Coupled generalized algebraic Riccati equations (CGAREs) involving pseudo inverse of a matrix are introduced. It is shown that the solvability of the LQ problem boils down to that of the CGAREs. However, the system of the CGAREs is hard to treat. To overcome this difficulty, the corresponding semidefinite programming (SDP) and related duality are utilized. Several implication relations among the SDP complementary duality, the existence of the solution to the CGAREs and the optimality of LQ problem are established. A numerical procedure that provides a thorough treatment of the LQ problem via primal-dual SDP is presented: it identifies a stabilizing optimal feedback control or determines that the LQ problem has no optimal solution
Starting Page	636
Ending Page	640
File Size	138681
Page Count	5
File Format	PDF
ISBN	1424403324
DOI	10.1109/WCICA.2006.1712419
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2006-06-21
Publisher Place	China
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Stochastic processes Riccati equations Costs Symmetric matrices Mathematics Linear matrix inequalities Mathematical programming Feedback control Stability Argon complementary dual Stochastic LQ control mean-square stability coupled generalized algebraic Riccati equations semidefinite programming
Content Type	Text
Resource Type	Article

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