Journal of Global Optimization

, Volume 23, Issue 3–4, pp 245–265 | Cite as

Discrete-time Indefinite LQ Control with State and Control Dependent Noises

  • M. Ait Rami
  • X. Chen
  • X.Y. Zhou
Article

Abstract

This paper deals with the discrete-time stochastic LQ problem involving state and control dependent noises, whereas the weighting matrices in the cost function are allowed to be indefinite. In this general setting, it is shown that the well-posedness and the attainability of the LQ problem are equivalent. Moreover, a generalized difference Riccati equation is introduced and it is proved that its solvability is necessary and sufficient for the existence of an optimal control which can be either of state feedback or open-loop form. Furthermore, the set of all optimal controls is identified in terms of the solution to the proposed difference Riccati equation.

Indefinite stochastic LQ control Discrete time Multiplicative noise Generalized difference Riccati equation Linear matrix inequality 

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Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • M. Ait Rami
    • 1
  • X. Chen
    • 1
  • X.Y. Zhou
    • 1
  1. 1.Department of Systems Engineering and Engineering ManagementThe Chinese University of Hong KongShatinHong Kong

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