Indefinite LQ optimal control with equality constraint for discrete-time uncertain systems

  • Yuefen Chen
  • Yuanguo ZhuEmail author
Original Paper Area 4


Based on uncertainty theory, this paper studies a kind of discrete-time uncertain linear quadratic (LQ) optimal control with equality constraint for the terminal state, allowing the state and control weighting matrices in the cost function to be indefinite. First, we transform the uncertain LQ optimal control problem into an equivalent deterministic optimal control problem. Then, a necessary condition for the existence of optimal linear state feedback control is presented by means of matrix minimum principle. Moreover, the well-posedness of the uncertain LQ problem is proved by applying the technique of completing squares. Finally, an example is provided to demonstrate the effectiveness of our theoretical results.


Indefinite LQ optimal control Equality constraint Discrete-time uncertain systems Constrained difference equation 

Mathematics Subject Classification

49J21 49K21 93B52 93C55 



This work is supported by the National Natural Science Foundation of China (No. 61273009).


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Copyright information

© The JJIAM Publishing Committee and Springer Japan 2016

Authors and Affiliations

  1. 1.School of ScienceNanjing University of Science and TechnologyNanjingChina
  2. 2.College of Mathematics and Information ScienceXinyang Normal UniversityXinyangChina

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