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Journal of Control Science and Engineering
Volume 2016, Article ID 7241390, 10 pages
Research Article

Indefinite LQ Optimal Control with Terminal State Constraint for Discrete-Time Uncertain Systems

1School of Science, Nanjing University of Science and Technology, Nanjing 210094, China
2College of Mathematics and Information Science, Xinyang Normal University, Xinyang 464000, China

Received 25 November 2015; Accepted 26 January 2016

Academic Editor: Petko Petkov

Copyright © 2016 Yuefen Chen and Minghai Yang. 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.


Uncertainty theory is a branch of mathematics for modeling human uncertainty based on the normality, duality, subadditivity, and product axioms. This paper studies a discrete-time LQ optimal control with terminal state constraint, whereas the weighting matrices in the cost function are indefinite and the system states are disturbed by uncertain noises. We first transform the uncertain LQ problem into an equivalent deterministic LQ problem. Then, the main result given in this paper is the necessary condition for the constrained indefinite LQ optimal control problem by means of the Lagrangian multiplier method. Moreover, in order to guarantee the well-posedness of the indefinite LQ problem and the existence of an optimal control, a sufficient condition is presented in the paper. Finally, a numerical example is presented at the end of the paper.