A Chain-Scattering Approach to LMI Multi-objective Control

International audienceThis paper revisits, from a chain-scattering perspective, the LMI solution based on Youla-Kucera parametrisation of the general multi-objective control problem. The conceptual and computational advantages of the chain-scattering formalism are demonstrated by allowing a more direct derivation of some known results as well as by hinting to some new research directions

Inverse skull conductivity estimation problems from EEG data

International audienceA fundamental problem in theoretical neurosciences is the inverse problem of source localization, which aims at locating the sources of the electric activity of the functioning human brain using measurements usually acquired by non-invasive imaging techniques, such as the electroencephalography (EEG). EEG measures the effect of the electric activity of active brain regions through values of the electric potential furnished by a set of electrodes placed at the surface of the scalp and serves for clinical (location of epilepsy foci) and functional brain investigation. The inverse source localization problem in EEG is influenced by the electric conductivities of the several head tissues and mostly by the conductivity of the skull. The human skull isa bony tissue consisting of compact and spongy bone compartments, whose shape and size vary over the age and the individual’s anatomy making difficult to accurately model the skull conductivity

Boundary control and observation of some one-dimensional vibrating structures : regularity and stabilization

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Active contour segmentation with a parametric shape prior: Link with the shape gradient

International audienceActive contours are adapted to image segmentation by energy minimization. The energies often exhibit local minima, requiring regularization. Such an a priori can be expressed as a shape prior and used in two main ways: (1) a shape prior energy is combined with the segmentation energy into a trade-off between prior compliance and accuracy or (2) the segmentation energy is minimized in the space defined by a parametric shape prior. Methods (1) require the tuning of a data-dependent balance parameter and methods (1) and (2) are often dedicated to a specific prior or contour representation, with the prior and segmentation aspects often meshed together, increasing complexity. A general framework for category (2) is proposed: it is independent of the prior and contour representations and it separates the prior and segmentation aspects. It relies on the relationship shown here between the shape gradient, the prior-induced admissible contour transformations, and the segmentation energy minimization

Nudelman interpolation, parametrizations of lossless functions and balanced realizations

We investigate the parametrization issue for discrete-time stable all-pass multivariable systems by means of a Schur algorithm involving a Nudelman interpolation condition. A recursive construction of balanced realizations is associated with it, that possesses a very good numerical behavior. Several atlases of charts or families of local parametrizations are presented and for each atlas a chart selection strategy is proposed. The last one can be viewed as a nice mutual encoding property of lossless functions and turns out to be very efficient. These parametrizations allow for solving optimization problems within the fields of system identification and optimal control

Identification de fissures droites depuis des mesures frontière incomplètes

Nous nous intéressons à la détection et à l'identification de fissures rectilignes à l'intérieur d'un conducteur isotrope plan (2D) à partir de mesures de la solution du problème de Neumann pour le Laplacien effectuées sur une partie seulement de la frontière extérieure du domaine. Nous procédons d'abord à l'extension à toute la frontière d'une estimation de la trace de la solution, au moyen de méthodes constructives d'analyse complexe et d'approximation issues de [13], puis à la localisation de la fissure, en utilisant les algorithmes proposés dans [17]

Shape sensitivity analysis in the Maxwell's equations

International audienceThe shape sensitivity analysis for hyperbolic problems yields some specific complications due to the hyperbolic regularity, or the lack thereof. In previous works we investigated the wave equation and came up with some shape sensistivity results. In this paper we investigate sensitivity of the solutions to the Maxwell equation with respect to the shape of the domain. We explicit a derivative with respect to a deformation parameter. The transport of the free divergence property requires a specific shape different quotient that is not necessary in the scalar case

A convergent finite element scheme for a wave equation with a moving boundary

International audienceWe wish to consider in this paper the numerical approximation of the solution of a wave equation when the boundaries of the spatial domain are moving. This problem has many practical applications in engineering science. One encounters wave systems in evolving domains in widely disseminated situations, such that rolling or unrolling antennas of space satellites, decoding the sound waves emitted by moving underwater objects or simulating the displacement of crane cables. In order to obtain computer simulations of this situations, one may try to make use of the following idea: a first discretization of the partial differential equation with respect to the space variable leads to a second order ordinary differential system M(h)q(t) + K(h)q(t) = F(t). The discretization parameter h gives typically the size of a cell, the number of such cells being held constant during the simulation. When the domain evolves with the time, the parameter h is allowed to vary, and one has to solve M(h(t))q(t) + K(h(t))q = F(t). We shall give evidence in this paper that the results given by such methods are false, as opposed to those obtained by using the concept of convected dense family defined in [2]. One may find in this reference a new proof of the existence of solution for the continuous problem which generalizes the Galerkin method on basis convected from OMEGA(t) to OMEGA0. This approach gives a practical way to generate the convergent numerical solutions we are looking for

Inverse source problem in a 3D ball from best meromorphic approximation on 2D slices

International audienceWe show that the inverse monopolar or dipolar source problem in a 3D ball from overdetermined Dirichlet-Neumann data on the boundary sphere reduces to a family of 2D inverse branchpoint problems in cross sections of the sphere, at least when there are finitely many sources. We adapt from [7] an approach to these 2D inverse problem which is based on meromorphic approximation, and we present numerical results