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Mathematical Problems in Engineering
Volume 2014, Article ID 278142, 9 pages
Research Article

Discrete-Time Indefinite Stochastic Linear Quadratic Optimal Control with Second Moment Constraints

1College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao 266590, China
2College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China

Received 1 April 2014; Accepted 29 April 2014; Published 18 May 2014

Academic Editor: Xuejun Xie

Copyright © 2014 Weihai Zhang and Guiling Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper studies the discrete-time stochastic linear quadratic (LQ) problem with a second moment constraint on the terminal state, where the weighting matrices in the cost functional are allowed to be indefinite. By means of the matrix Lagrange theorem, a new class of generalized difference Riccati equations (GDREs) is introduced. It is shown that the well-posedness, and the attainability of the LQ problem and the solvability of the GDREs are equivalent to each other.