Contrôle optimal pour les problèmes de contrôlabilité des systèmes distribués à données manquantes

We consider the optimal control of general heat governed by an operator depend on an unknown parameter and with missing boundary condition. Using the notion of no-regret and low-regret control we prove that we can bring the average of the state of our model to a desired state. Then by means of Euler-Lagrange first order optimality condition, we expressed the optimal control in term of average of an appropriate adjoint state that we characterize by an optimality system. The main tools are the Lebesgue dominated convergence theorem and an appropriate Hilbert space endowed with a norm containing the average of the state.

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“…Step 1. We prove that (u γ , y γ ) satisfies (6). Let D(Q) being the set of functions of class C ∞ on Q with compact support.…”

Section: Existence and Characterization Of The Low-regret Controlmentioning

confidence: 95%

Optimal control of averaged state of a parabolic equation with missing boundary condition

Mophou

Tiomela

Ali

2018

International Journal of Control

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“…But, the above system does not admit a solution for arbitrary data (3). Indeed, in the case of final data, i.e.…”

Section: Preliminariesmentioning

confidence: 96%

“…Instead of the regularization for the backward ill-posed approach, we here use the null-controllability approach in Dorville et al [3] for the regular heat equation (of incomplete data). With the low-regret method, we obtain at the end an optimality system for the backward ill-problem.…”

Section: The Controllability Approachmentioning

confidence: 99%

“…Then the goal is to study the optimal control of this controlled system. The question of control for controllability problems of incomplete data is new, and was treated in detail by Dorville [1], and by Dorville et al [3] very recently. We recall a variational method which ensures the existence and uniqueness selection of a solution for (39)(40).…”

Section: The Controllability Approachmentioning

confidence: 99%

See 1 more Smart Citation

On the control of ill-posed distributed parameter systems

Dorville¹,

Nakoulima²,

Omrane³

2007

ESAIM: Proc.

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We show that the so-called low-regret (or least-regret) control by J. L. Lions [8] fits on the control of ill-posed problems. At each time, we give the characterization of the so-called no-regret control by means of singular optimality systems. For the backward heat ill-posed problem, no Slater hypothesis is assumed on the admissible set of controls U ad . This work is two pieces, and two methods are considered : the regularization method and the nullcontrollability method. For the first method, a zero order corrector is used, while for the second method, the passage to the limit is easy. The results presented here generalize the works in [2, 3] to the no-regret control.Résumé. On montre que le contrôleà moindres regrets de J. L. Lions [8] est bien adapté pour le contrôle des des problèmes mal posés. A chaque fois, on donne une caractérisation du contrôle sans regret par le moyen de systèmes d'optimalité singuliers. Pour le problème de chaleur rétrograde mal posé, aucune hypothèse de type Slater sur l'ensemble des contrôles admissibles U ad n'est nécessaire. Ce travail est divisé en deux parties, et deux méthodes sont considérées: la méthode de régularisation et celle de la contrôlabilitéà zéro. Pour la première méthode, un correcteur d'ordre zéro est utilisé, alors que pour la seconde méthode le passageà la limite est simple. Les résultats présentés ici généralisent les travaux dans [2, 3] au contrôle sans regret.

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“…In [10], O. Nakolima, R. Dorville, and A. Omrane studied how the no regret control can be extended to the hyperbolic case. They also generalized these concepts in the case of ill-posed deterministic problems, without assuming Slater's condition [8,9]. In [11], Hafdallah A, and Ayadi A applied no regret and low regret concepts to control a thermoelastic body with missing initial conditions.…”

Section: Setting the Problemmentioning

confidence: 99%

Optimal Control of a Partially Known Coupled System of BOD and DO

Laouar¹,

Àyadi²,

Hafdallah³

2021

Int. J. Anal. Appl.

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The work presented in this paper is concerned with the organic pollution problem and water quality valuation. Biochemical oxygen demand has been used to evaluate the quality of water. If organic matter is present the dissolved oxygen is consumed. This article considers an optimal control problem of coupled system with missing initial conditions, which presents the relation between the biochemical oxygen demand and the dissolved oxygen. The main objective is to control the concentration of dissolved oxygen using the information given in the biochemical oxygen demand equation. The main tool used to characterize the optimal control of the investigate system under the Pareto control formulation.

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Contrôle optimal pour les problèmes de contrôlabilité des systèmes distribués à données manquantes

Cited by 6 publications

References 2 publications

Optimal control of averaged state of a parabolic equation with missing boundary condition

Optimal control of averaged state of a parabolic equation with missing boundary condition

On the control of ill-posed distributed parameter systems

Optimal Control of a Partially Known Coupled System of BOD and DO

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