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Search Results: 1 - 10 of 401383 matches for " Dambrine M. "
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Feedback control of time-delay systems with bounded control and state
Dambrine M.,Richard J. P.,Borne P.
Mathematical Problems in Engineering , 1995,
Abstract: This paper is concerned with the problem of stabilizing linear time-delay systems under state and control linear constraints. For this, necessary and sufficient conditions for a given non-symmetrical polyhedral set to be positively invariant are obtained. Then existence conditions of linear state feedback control law respecting the constraints are established, and a procedure is given in order to calculate such a controller. The paper concerns memoryless controlled systems but the results can be applied to cases of delayed controlled systems. An example is given.
Feedback control of time-delay systems with bounded control and state
M. Dambrine,J. P. Richard,P. Borne
Mathematical Problems in Engineering , 1995, DOI: 10.1155/s1024123x95000081
Shape optimization for quadratic functionals and states with random right-hand sides
M. Dambrine,C. Dapogny,H. Harbrecht
Mathematics , 2015,
Abstract: In this work, we investigate a particular class of shape optimization problems under uncertainties on the input parameters. More precisely, we are interested in the minimization of the expectation of a quadratic objective in a situation where the state function depends linearly on a random input parameter. This framework covers important objectives such as tracking-type functionals for elliptic second order partial differential equations and the compliance in linear elasticity. We show that the robust objective and its gradient are completely and explicitly determined by low-order moments of the random input. We then derive a cheap, deterministic algorithm to minimize this objective and present model cases in structural optimization.
Minimization of the ground state of the mixture of two conducting materials in a small contrast regime
C. Conca,M. Dambrine,R. Mahadevan,D. Quintero
Mathematics , 2014,
Abstract: We consider the problem of distributing two conducting materials with a prescribed volume ratio in a given domain so as to minimize the first eigenvalue of an elliptic operator with Dirichlet conditions. The gap between the two conductivities is assumed to be small (low contrast regime). For any geometrical configuration of the mixture, we provide a complete asymptotic expansion of the first eigenvalue. We then consider a relaxation approach to minimize the second order approximation with respect to the mixture. We present numerical simulations in dimensions two and three.
Colloque Kubrick, les films, les musiques
Serge Dambrine
Transatlantica : Revue d'études Américaines , 2012,
Abstract: SCRIPT, centre de recherche en émergence à l’Université d’évry, con u comme une plateforme des arts engagés très contemporains, organisait au printemps sa première manifestation scientifique. Alors que la Cinémathèque Fran aise inaugurait l’exposition Stanley Kubrick , américanistes, filmologues, musicologues et praticiens de la communication se réunissaient sur le campus d’évry pour examiner ensemble l’ uvre du grand cinéaste mort en 1999.Photographe et joueur d'échecs, féru de lecture au...
Multiscale expansion and numerical approximation for surface defects
Bonnaillie-No?l V.,Brancherie D.,Dambrine M.,Hérau F.
ESAIM : Proceedings , 2011, DOI: 10.1051/proc/201133003
Abstract: This paper is a survey of articles [5, 6, 8, 9, 13, 17, 18]. We are interested in the influence of small geometrical perturbations on the solution of elliptic problems. The cases of a single inclusion or several well-separated inclusions have been deeply studied. We recall here techniques to construct an asymptotic expansion. Then we consider moderately close inclusions, i.e. the distance between the inclusions tends to zero more slowly than their characteristic size. We provide a complete asymptotic description of the solution of the Laplace equation. We also present numerical simulations based on the multiscale superposition method derived from the first order expansion (cf [9]). We give an application of theses techniques in linear elasticity to predict the behavior till rupture of materials with microdefects (cf [6]). We explain how some mathematical questions about the loss of coercivity arise from the computation of the profiles appearing in the expansion (cf [8]). Nous faisons ici une synthèse des articles [5, 6, 8, 9, 13, 17, 18]. On s’intéresse à l’influence de petites perturbations géométriques sur la solution de problèmes elliptiques. Les cas d’une inclusion isolée ou de plusieurs bien séparées ont été largement étudiés. Nous considérons plus précisément le cas où la distance entre deux inclusions tend vers zéro mais reste grande par rapport à leur taille caractéristique. Nous donnons un développement asymptotique multi-échelle complet de la solution de l’équation de Laplace dans la situation de deux inclusions. Nous présentons également quelques simulations numériques basées sur une méthode de superposition multi-échelle provenant du développement au premier ordre (cf [9]). Nous étendons ces techniques aux équations de l’élasticité linéaire afin de prédire le comportement à rupture de certains matériaux présentant des micro-défauts (cf [6]). Nous verrons également comment le calcul numérique des profils intervenant dans le développement asymptotique soulève des questions mathématiques liées à la perte de coercivité des problèmes approchés (cf [8]).
A remark on precomposition on $\sH^{1/2}(S^1)$ and $\eps$-identifiability of disks in tomography
Marc Dambrine,Djalil Kateb
Mathematics , 2006,
Abstract: We consider the inverse conductivity problem with one measurement for the equation $div((\sigma\_1+(\sigma\_2-\sigma\_1)\chi\_D)\nabla{u})=0$ determining the unknown inclusion $D$ included in $\Omega$. We suppose that $\Omega$ is the unit disk of $\mathbb{R}^2$. With the tools of the conformal mappings, of elementary Fourier analysis and also the action of some quasi-conformal mapping on the Sobolev space $\sH^{1/2}(S^1)$, we show how to approximate the Dirichlet-to-Neumann map when the original inclusion $D$ is a $\epsilon-$ approximation of a disk. This enables us to give some uniqueness and stability results.
Stability in shape optimization with second variation
Marc Dambrine,Jimmy Lamboley
Mathematics , 2014,
Abstract: We are interested in the question of stability in the field of shape optimization. Precisely, we prove that under structural assumptions on the hessian of the considered shape functions, the necessary second order minimality conditions imply that the shape hessian is coercive for a given norm. Moreover, under an additional continuity condition for the second order derivatives, we derive precise optimality results in the class of regular perturbations of a domain. These conditions are quite general and are satisfied for the volume, the perimeter, the torsional rigidity and the first Dirichlet eigenvalue of the Laplace operator. As an application, we provide non trivial examples of inequalities obtained in this way.
Genetic analysis of a divergent selection for resistance to Rous sarcomas in chickens?. This article is dedicated to the memory of Pierrick Thoraval (1960–2000).
Marie-Hélène Laan, Denis Soubieux, Laurence Mérat, Danièle Bouret, Gillette Luneau, Ginette Dambrine, Pierrick Thoraval
Genetics Selection Evolution , 2004, DOI: 10.1186/1297-9686-36-1-65
Abstract: (To access the full article, please see PDF)
On second order shape optimization methods for electrical impedance tomography
Lekbir Afraites,Marc Dambrine,Djalil Kateb
Mathematics , 2007,
Abstract: This paper is devoted to the analysis of a second order method for recovering the \emph{a priori} unknown shape of an inclusion $\omega$ inside a body $\Omega$ from boundary measurement. This inverse problem - known as electrical impedance tomography - has many important practical applications and hence has focussed much attention during the last years. However, to our best knowledge, no work has yet considered a second order approach for this problem. This paper aims to fill that void: we investigate the existence of second order derivative of the state $u$ with respect to perturbations of the shape of the interface $\partial\omega$, then we choose a cost function in order to recover the geometry of $\partial \omega$ and derive the expression of the derivatives needed to implement the corresponding Newton method. We then investigate the stability of the process and explain why this inverse problem is severely ill-posed by proving the compactness of the Hessian at the global minimizer.
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