Journal Article

Linear quadratic control problem with a terminal convex constraint for discrete-time distributed systems

L. Chraïbi, J. Karrakchou, M. Rachik and A. Ouansafi

in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 23, issue 3, pages 347-370
Published in print September 2006 | ISSN: 0265-0754
Published online September 2006 | e-ISSN: 1471-6887 | DOI: http://dx.doi.org/10.1093/imamci/dni063
Linear quadratic control problem with a terminal convex constraint for discrete-time distributed systems

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The present work deals with the linear quadratic control problem for a discrete distributed system with terminal convex constraint. Using techniques of perturbation by feedback, it is shown that the resolution of the considered problem is equivalent to that of a controllability, one so-called Extended Exact Controllability with time-varying operators. The Hilbert uniqueness method approach is then extended to this case to provide an explicit form for the optimal control. In the same framework, the inequality constraint case is examined for which a practical numerical resolution is given. Finally, the results obtained are used to treat a minimum-time reachability problem.

Keywords: convex constraint; Extended Exact Controllability Problem; feedback law; perturbed state equation; optimal control

Journal Article.  0 words. 

Subjects: Mathematics

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