Contrôlabilité à zéro avec contraintes sur le contrôle

Nakoulima, Ousseynou

doi:10.1016/j.crma.2004.07.005

Cited by 23 publications

(25 citation statements)

References 2 publications

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“…Thus, if we suppose that, for instance v 1 = 0 on (0, T ) × ω, this lemma implies that To obtain a control satisfying the constraints (3.5), we follow the method presented in [15] and used in [6]. We will prove an improved observability inequality.…”

Section: Consequently A(t ) = 0 and θ(T ) = 0 If And Only Ifmentioning

confidence: 99%

Local null controllability of a two-dimensional fluid-structure interaction problem

Boulakia

Osses

2007

ESAIM: COCV

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Abstract.In this paper, we prove a controllability result for a fluid-structure interaction problem.In dimension two, a rigid structure moves into an incompressible fluid governed by Navier-Stokes equations. The control acts on a fixed subset of the fluid domain. We prove that, for small initial data, this system is null controllable, that is, for a given T > 0, the system can be driven at rest and the structure to its reference configuration at time T . To show this result, we first consider a linearized system. Thanks to an observability inequality obtained from a Carleman inequality, we prove an optimal controllability result with a regular control. Next, with the help of Kakutani's fixed point theorem and a regularity result, we pass to the nonlinear problem.Mathematics Subject Classification. 35Q30, 93C20.

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Section: Consequently A(t ) = 0 and θ(T ) = 0 If And Only Ifmentioning

confidence: 99%

Local null controllability of a two-dimensional fluid-structure interaction problem

Boulakia

Osses

2007

ESAIM: COCV

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“…3). In Section 5, we give an application of the above results to the sentinels theory of Lions as revisited in [16].…”

Section: Remarkmentioning

confidence: 99%

“…We also refer to Barbu [1], Doubova et al [5], Fabre et al [6], Fernández-Cara [7], Fernández-Cara and Guerrero [8], Zuazua [18,20], and their bibliography for other related controllability problems. The null-controllability problem (1), (4) and (5) in the case K = {0} has been studied by the author in [16] when K is of finite dimension. In this case, some compatibility conditions are requiered for controllability to hold.…”

Section: Remarkmentioning

confidence: 99%

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

Nakoulima

2007

ESAIM: COCV

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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 control point 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)].Mathematics Subject Classification. 35K05, 35K15, 35K20, 49J20, 93B05.

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“…The definition (4) extends the one by Lions to the case where the observation and the control have different supports. This point of view (where ω = O) has been considered for the first time by Nakoulima in [15]. Here we avoid the trivial solution.…”

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confidence: 99%

A method for detecting pollution in dissipative systems with incomplete data.

2007

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Abstract. Modelling environmental problems leads to mathematical systems with missing data. For instance, weather problems have generally missing initial conditions. The paper is concerned with identifying pollution terms arising in the state equation of some dissipative system with incomplete initial condition. To this aim the so-called sentinel method is used. Here, the problem of determining a sentinel is equivalent to a null-controllability problem for which Carleman inequalities are revisited.Résumé. La modélisation des problèmes environmentaux conduità des systèmes mathématiquesà données manquantes. C'est le cas par exemple des problèmes de météorologie où l'on ne connaît jamais la donnée initiale. Nous sommes concernés dans cet article, par l'identification des termes de pollution présents dans l'équation d'état d'un système dissipatifà donnée initiale incomplète. Dans ce but, la méthode des sentinelles de Lions est utilisée. Ici, le problème de détermination d'une sentinelle estéquivalentà un problème de contrôlabilitéà zéro pour lequel on donne des estimations de type Carleman.

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Contrôlabilité à zéro avec contraintes sur le contrôle

Cited by 23 publications

References 2 publications

Local null controllability of a two-dimensional fluid-structure interaction problem

Local null controllability of a two-dimensional fluid-structure interaction problem

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

A method for detecting pollution in dissipative systems with incomplete data.

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