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649 results on '"Coron, Jean-Michel"'

645. Exponential stability of PI control for Saint-Venant equations with a friction term

Author

Georges Bastin, Jean-Michel Coron, Centre for Systems Engineering and Applied Mechanics (CSAM), Université Catholique de Louvain = Catholic University of Louvain (UCL), Sorbonne Université (SU), Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Control And GEometry (CaGE ), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), ANR-15-CE23-0007,Finite4SoS,Commande et estimation en temps fini pour les Systèmes de Systèmes(2015), Coron, Jean-Michel, Fondements du numérique - Commande et estimation en temps fini pour les Systèmes de Systèmes - - Finite4SoS2015 - ANR-15-CE23-0007 - AAPG2015 - VALID, Université Catholique de Louvain (UCL), and UCL - SST/ICTM/INMA - Pôle en ingénierie mathématique

Subjects
Lyapunov stability, 0209 industrial biotechnology, 010102 general mathematics, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], 02 engineering and technology, 01 natural sciences, Hyperbolic systems, Term (time), 020901 industrial engineering & automation, Exponential stability, Pi, Applied mathematics, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], 0101 mathematics, Shallow water equations, Mathematics
Abstract

International audience; We consider open channels represented by Saint-Venant equations that are monitored and controlled at the downstream boundary and subject to unmeasured flow disturbances at the upstream boundary. We address the issue of feedback stabilization and disturbance rejection under Proportional-Integral (PI) boundary control. For channels with uniform steady states, the analysis has been carried out previously in the literature with spectral methods as well as with Lyapunov functions in Riemann coordinates. In this article, our main contribution is to show how the analysis can be extended to channels with non-uniform steady states with a Lyapunov function in physical coordinates.

Published
2019

646. Null controllability and finite time stabilization for the heat equations with variable coefficients in space in one dimension via backstepping approach

Author

Jean-Michel Coron, Hoai-Minh Nguyen, Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Chair of Analysis and Applied Mathematics [Lausanne] (CAMA), Department of mathematics [Lausanne], School of Basic Sciences [Lausanne], Ecole Polytechnique Fédérale de Lausanne (EPFL)-Ecole Polytechnique Fédérale de Lausanne (EPFL)-School of Basic Sciences [Lausanne], Ecole Polytechnique Fédérale de Lausanne (EPFL)-Ecole Polytechnique Fédérale de Lausanne (EPFL), European Project: 266907,EC:FP7:ERC,ERC-2010-AdG_20100224,CPDENL(2011), Coron, Jean-Michel, and Control of partial differential equations and nonlinearity - CPDENL - - EC:FP7:ERC2011-05-01 - 2016-04-30 - 266907 - VALID

Subjects
backstepping, 0209 industrial biotechnology, 02 engineering and technology, Space (mathematics), 01 natural sciences, Kernel (linear algebra), 020901 industrial engineering & automation, Mathematics (miscellaneous), Dimension (vector space), Control theory, 0101 mathematics, Mathematics, Variable (mathematics), Null controllability, heat equation, Mechanical Engineering, 010102 general mathematics, Null (mathematics), Mathematical analysis, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], Controllability, Backstepping, Heat equation, MSC: 93B05, 93B17, 93B52, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], time-varying feedback laws, Analysis, stabilization in finite time
Abstract

Using the backstepping approach we recover the null controllability for the heat equations with variable coefficients in space in one dimension and prove that these equations can be stabilized in finite time by means of periodic time-varying feedback laws. To this end, on the one hand, we provide a new proof of the well-posedness and the “optimal” bound with respect to damping constants for the solutions of the kernel equations; this allows one to deal with variable coefficients, even with a weak regularity of these coefficients. On the other hand, we establish the well-posedness and estimates for the heat equations with a nonlocal boundary condition at one side.

Published
2015

647. Boundary control of quasi-linear hyperbolic initial boundary-value problems

Author

de Halleux, Jonathan, UCL - FSA/INMA - Département d'ingénierie mathématique, Dochain, Denis, Coron, Jean-Michel, Blondel, Vincent, d'Andréa-Novel, Brigitte, Winkin, Joseph, and Bastin, Georges

Subjects
Shallow water equations, Saint-Venant, Control, Partial differential equations, Stabilization
Abstract

This thesis presents different control design approaches for stabilizing networks of quasi-linear hyperbolic partial differential equations. These equations are usually conservative which gives them interesting properties to design stabilizing control laws. Two main design approaches are developed: a methodology based on entropies and Lyapunov functions and a methodology based on the Riemann invariants. The stability theorems are illustrated using numerical simulations. Two practical applications of these methodologies are presented. Netword of navigation channels are modelled using Saint-Venant equations (also known as the Shallow Water Equations). The stabilization problem of such system has an industrial importance in order to satisfy the navigation constraints and to optimize the production of electricity in hydroelectric plants, usually located at each hydraulic gates. A second application deals with the regulation of water waves in moving tanks. This problem is also modelled by a modified version of the shallow water equations and appears in a number of industrial fields which deal with liquid moving parts. (FSA 3)--UCL, 2004

Published
2004

648. Contrôlabilité exacte d'équations dispersives issues de la mécanique

Author

Crépeau, Emmanuelle, Laboratoire d'analyse numérique et EDP, Université Paris Sud Orsay, Université Paris Sud - Paris XI, and Coron Jean-Michel

Subjects
approximation numérique, HUM, contrôlabilité exacte d'un système non linéaire, "bonne" équation de Boussinesq, [MATH]Mathematics [math], bonne" équation de Boussinesq, EDP, équation de Korteweg-de Vries, contrôlabilité exacte d'un système linéaire
Abstract

Puel Jean-Pierre, président du jury; Raymond Jean-Pierre, Rouchon pierre, Tucsnak Marius, membres du jury;; In this thesis, we study the exact controllability of two dispersive equations, the Korteweg-de Vries equation and the "good" Boussinesq equation. First, for the Korteweg-de Vries equation, we extend a result of Rosier. We prove that for a critical length, the nonlinear equation is exactly controllable in a neighborhood of a small non null stationary solution. This study uses the Hilbert Uniqueness Method with the multiplier theory and a fixed point theorem. Secondly, we study the exact controllability of the "good" Boussinesq equation with two different boundary controls. We use again the Hilbert Uniqueness Method but with Ingham inequality. Lastly, we apply this method for a numerical approach of the controllability of the Boussinesq equation both for linear and nonlinear equations. The control is applied to the second spatial derivative, at the right endpoint.; Le sujet principal de cette thèse est l'étude de la contrôlabilité exacte de deux équations dispersives, l'équation de Korteweg-de Vries et la "bonne" équation de Boussinesq. En ce qui concerne l'équation de Korteweg-de Vrie, on étend un résultat de Rosier en montrant la contrôlabilité exacte en tout temps de l'équation non linéaire autour d'une solution stationnaire proche de zéro mais non nulle, ce pour des longueurs de domaine spatial critiques. Cette démonstration utilise en particulier la méthode d'unicité hilbertienne couplée avec la méthode des multiplicateurs et un théorème de point fixe. Ensuite, nous étudions le problème de la contrôlabilité exacte de l'équation de Boussinesq pour deux contrôles différents. On utilise également la méthode d'unicité hilbertienne pour ces problèmes en appliquant une inégalité de Ingham. On obtient ainsi un résultat de contrôlabilité exacte pour des temps arbitrairement petits. Nous implémentons ensuite cette méthode de facon numérique pour l'équation de Boussinesq avec un contrôle portant sur la dérivée seconde a droite, tant sur le problème linéaire que non linéaire.

Published
2002

649. Optimization of an amplification protocol for misfolded proteins by using relaxed control.

Author

Coron JM, Gabriel P, and Shang P

Subjects
Animals, Humans, Mathematical Concepts, Nonlinear Dynamics, Prion Diseases diagnosis, Protein Aggregates, Proteostasis Deficiencies diagnosis, Models, Molecular, Prions chemistry, Protein Folding
Abstract

We investigate an optimal control problem which arises in the optimization of an amplification technique for misfolded proteins. The improvement of this technique may play a role in the detection of prion diseases. The model consists in a linear system of differential equations with a nonlinear control. The appearance of oscillations in the numerical simulations is understood by using the Perron and Floquet eigenvalue theory for nonnegative irreducible matrices. Then to overcome the unsolvability of the optimal control, we relax the problem. In the two dimensional case, we solve explicitly the optimal relaxed control problem when the final time is large enough.

Published
2015
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