Perturbations à moindres regrets dans les systèmes distribués à données manquantes

Nakoulima, Ousseynou; Omrane, Amina; Vélin, Jean

doi:10.1016/s0764-4442(00)00263-9

Cited by 23 publications

(21 citation statements)

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“…Some of the results in this paper are summarized in [17]. The proofs in the present paper and the treatment of the evolution cases are new.…”

Section: Introduction Let V Be a Real Hilbert Space Of Dual V A ∈ mentioning

confidence: 87%

“…We improve the results of the work in [14] (and also [12]) of Lions by giving the precise optimality system for the low-regret control and by describing a number of applications. Thanks to a quadratic perturbation used by the authors in [17], the optimality system for the no-regret control appears clearly as the limit of a standard control problem.…”

Section: Introduction Let V Be a Real Hilbert Space Of Dual V A ∈ mentioning

confidence: 99%

See 1 more Smart Citation

On the Pareto Control and No-Regret Control for Distributed Systems with Incomplete Data

Nakoulima¹,

Omrane²,

Vélin

2003

SIAM J. Control Optim.

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Abstract. We discuss the control of distributed systems with incomplete data following the notion of no-regret control (or, equivalently, Pareto control) used by Lions in [C. R. Acad. Sci. Paris Ser. I Math., 302 (1986) In the first part, we prove that the perturbed system corresponds to a sequence of standard control problems and converges to the no-regret (or Pareto) control for which we obtain a singular optimality system. We give also some applications.In the second part, we show how the method can be extended to the evolution case. Equations of parabolic type, Petrowsky type, or hyperbolic type are considered.

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“…Some of the results in this paper are summarized in [17]. The proofs in the present paper and the treatment of the evolution cases are new.…”

Section: Introduction Let V Be a Real Hilbert Space Of Dual V A ∈ mentioning

confidence: 87%

Section: Introduction Let V Be a Real Hilbert Space Of Dual V A ∈ mentioning

confidence: 99%

On the Pareto Control and No-Regret Control for Distributed Systems with Incomplete Data

Nakoulima¹,

Omrane²,

Vélin

2003

SIAM J. Control Optim.

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“…The no-regret control is difficult to characterize in this present form (see [16]). Thus we define in the next section the low-regret control notion.…”

Section: Main Definitionsmentioning

confidence: 98%

“…To achieve the no-regret control, we give the precise optimality system for the low-regret control for the incomplete data population dynamics (1)-(2), using a quadratic perturbation by Nakoulima et al in [16] (see also [17]). Then, we give a characterization of the no-regret control which appears clearly as the limit of a standard control problem.…”

Section: Introductionmentioning

confidence: 99%

Optimal control for age-structured population dynamics of incomplete data

Jacob

Omrane²

2010

Journal of Mathematical Analysis and Applications

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We are concerned with the control question for linear age-structured population dynamics of incomplete initial data. More precisely, the initial population age distribution is supposed to be unknown. We here generalize the notion of no-regret control of Lions (1992) [10] to such singular population dynamics, following the method by Nakoulima, Omrane and Vélin (2000) [16]. We prove that the problem we are considering has a unique no-regret control that we characterize by a singular optimality system.

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“…We here use a method that we find well adapted: the low-regret control concept, introduced by Lions in the late 80s (see, e.g., [9,10] and the references therein). In [11,12], the control of distributed system with incomplete data is performed. The proof of the existence and 2 International Journal of Differential Equations characterization of the no-regret control is obtained as the limit of the low-regret control.…”

Section: Introductionmentioning

confidence: 99%