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Optimal control for distributed systems subjectto null-controllability. Application to discriminating sentinels

Published online by Cambridge University Press:  05 September 2007

Ousseynou Nakoulima
Ousseynou Nakoulima*
Affiliation:
Université Antilles-Guyane, Département de Mathématiques et Informatique, 97159 Pointe-à-Pitre, Guadeloupe, France; onakouli@univ-ag.fr
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Abstract

We consider a distributed system in which the state q is governed by a parabolic equation and a pair of controls v = (h,k) where h and k play two different roles: the control k is of controllability type while h expresses that the state q does not move too far from a given state. Therefore, it is natural to introduce the controlpoint of view. In fact, there are several ways to state and solve optimal control problems with a pair of controls h and k, in particular the Least Squares method with only one criteria for the pair (h,k) or the Pareto Optimal Control for multicriteria problems. We propose here to use the notion of Hierarchic Control. This notion assumes that we have two controls h, k where h will be the leader while k will be the follower. The main tool used to solve the null-controllability problem with constraints on the follower is an observability inequality of Carleman type which is “adapted” to the constraints. The obtained results are applied to the sentinels theory of Lions [Masson (1992)].

Keywords

Heat equationoptimal controlcontrollabilityCarleman inequalitiessentinels

Information

Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 13 , Issue 4 , October 2007, pp. 623 - 638
Copyright
© EDP Sciences, SMAI, 2007

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