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

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  • Shaowei Zhou
  • Weihai Zhang

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.

Suggested Citation

  • Shaowei Zhou & Weihai Zhang, 2012. "Discrete-Time Indefinite Stochastic LQ Control via SDP and LMI Methods," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-14, February.
    • Handle: RePEc:hin:jnljam:638762
    DOI: 10.1155/2012/638762
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    Cited by:

    1. Haoyu Dong & Changna Lu & Hongwei Yang, 2018. "The Finite Volume WENO with Lax–Wendroff Scheme for Nonlinear System of Euler Equations," Mathematics, MDPI, vol. 6(10), pages 1-17, October.

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