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IMA Journal of Mathematical Control and Information Advance Access published online on October 28, 2005
IMA Journal of Mathematical Control and Information, doi:10.1093/imamci/dni063
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© The author 2005. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Article

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

L. Chraïbi 1*, J. Karrakchou 2, M. Rachik 3, and A. Ouansafi 4

1 Ecole Nationale des Sciences Appliquées de Tanger, BP 1818, Tangier, Morocco
2 Ecole Mohammadia d'Ingénieurs, B P 765, Rabat, Morocco
3 Faculté des Sciences Benmsik, Casablanca, Morocco
4 Faculté des Sciences, BP 1014, Rabat, Morocco

* To whom correspondence should be addressed.
L. Chraïbi, E-mail: l_chraibi{at}wanadoo.ma


  Abstract

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.
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