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Indefinite LQ Control for Discrete-Time Stochastic Systems via Semidefinite Programming

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  • Shaowei Zhou
  • Weihai Zhang

Abstract

This paper is concerned with a discrete-time indefinite stochastic LQ problem in an infinite-time horizon. A generalized stochastic algebraic Riccati equation (GSARE) that involves the Moore-Penrose inverse of a matrix and a positive semidefinite constraint is introduced. We mainly use a semidefinite-programming- (SDP-) based approach to study corresponding problems. Several relations among SDP complementary duality, the GSARE, and the optimality of LQ problem are established.

Suggested Citation

  • Shaowei Zhou & Weihai Zhang, 2012. "Indefinite LQ Control for Discrete-Time Stochastic Systems via Semidefinite Programming," Mathematical Problems in Engineering, Hindawi, vol. 2012, pages 1-14, January.
    • Handle: RePEc:hin:jnlmpe:674087
    DOI: 10.1155/2012/674087
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