Journal of Applied Mathematics

Discrete-Time Indefinite Stochastic LQ Control via SDP and LMI Methods

Shaowei Zhou and Weihai Zhang

Full-text: Open access

Abstract

This paper studies a discrete-time stochastic LQ problem over an infinite time horizon with state-and control-dependent noises, whereas the weighting matrices in the cost function are allowed to be indefinite. We mainly use semidefinite programming (SDP) and its duality to treat corresponding problems. Several relations among stability, SDP complementary duality, the existence of the solution to stochastic algebraic Riccati equation (SARE), and the optimality of LQ problem are established. We can test mean square stabilizability and solve SARE via SDP by LMIs method.

Article information

Source
J. Appl. Math., Volume 2012 (2012), Article ID 638762, 14 pages.

Dates
First available in Project Euclid: 17 October 2012

Permanent link to this document
https://projecteuclid.org/euclid.jam/1350479384

Digital Object Identifier
doi:10.1155/2012/638762

Mathematical Reviews number (MathSciNet)
MR2880836

Zentralblatt MATH identifier
1235.93266

Citation

Zhou, Shaowei; Zhang, Weihai. Discrete-Time Indefinite Stochastic LQ Control via SDP and LMI Methods. J. Appl. Math. 2012 (2012), Article ID 638762, 14 pages. doi:10.1155/2012/638762. https://projecteuclid.org/euclid.jam/1350479384


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