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10. Stabilisation avec retard de l'équation de Korteweg-de Vries sur un réseau de type étoile

Author

Hugo Parada, Emmanuelle Crépeau, Christophe Prieur, Equations aux Dérivées Partielles (EDP), Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), Laboratoire de Mathématiques de Versailles (LMV), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), GIPSA - Infinite Dimensional Dynamics (GIPSA-INFINITY), GIPSA Pôle Automatique et Diagnostic (GIPSA-PAD), Grenoble Images Parole Signal Automatique (GIPSA-lab), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Grenoble Images Parole Signal Automatique (GIPSA-lab), and ANR-19-P3IA-0003,MIAI,MIAI @ Grenoble Alpes(2019)

Subjects
KdV equation, Control and Optimization, Star-Shaped Network, Control and Systems Engineering, delay, Applied Mathematics, Signal Processing, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], stabilization, Mathematics Subject Classification (2010)35Q53·35B35·35R02
Abstract

International audience; In this work we deal with the exponential stability of the nonlinear Kortewegde Vries (KdV) equation on a finite star-shaped network in the presence of delayed internal feedback. We start by proving the well-posedness of the system and some regularity results. Then we state an exponential stabilization result using a Lyapunov function by imposing small initial data and a restriction over the lengths. In this part also, we are able to obtain an explicit expression for the rate of decay. Then we prove the exponential stability of the solutions without restriction on the lengths and for small initial data, this result is based on an observability inequality. After that, we obtain a semi-global stabilization result working directly with the nonlinear system. Next we study the case where it may happen that a control domain with delay is outside of the control domain without delay. In that case, we obtain also a local exponential stabilization result. Finally, we present some numerical simulations in order to illustrate the stabilization.

Published
2022
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16. Projections d’habitants face à des données climatiques localisées : Ruse rétrospective pour un territoire apprenant

Author

Emmanuelle Crépeau and Dominique Bachelart

Subjects
Social Sciences and Humanities, éducation des adultes aux changements climatiques, Sciences Humaines et Sociales, atelier prospectif territorial, participation des habitants
Abstract

L’article présente les actions conduites par un Parc naturel régional (PNR) français avec des habitants de son territoire pour les sensibiliser aux changements climatiques. La nature même des enjeux climatiques soulève de délicates questions stratégiques en matière de communication et d’information de la population. Parmi toutes les démarches menées par le PNR pour la diffusion des données scientifiques élaborées sur les effets locaux des changements climatiques, l’analyse porte spécifiquement sur l’animation « d’ateliers de prospective territoriale » conduits avec des groupes d’habitants pour initier une dynamique collective et identifier les enjeux engageant l’avenir de l’espace géographique du PNR. La réflexion est issue du dialogue et d’une co-écriture entre une chargée de mission « éducation » et une chercheuse en observation participante sur trois des ateliers. La philosophie des ateliers se fonde sur la projection sur l’avenir articulant savoirs citoyens expérientiels et connaissances individuelles sur le climat, et les savoirs scientifiques et scénarisations contrastées et hypothétiques de tendances sur le territoire afin de construire une vision débattue voire partagée des actions à mener. Le détour par une projection en 2070, à travers les co-productions des habitants dans ces ateliers, est expérimenté comme « ruse rétrospective » : conscientisant les scénarii de l’inacceptable, pour définir collectivement les enjeux à relever. Il a pour effet pour les participants de se positionner dans le présent comme plus proactif face à l’avenir. L’atelier met en évidence la nécessité de structures institutionnelles propices à la délibération et un territoire « apprenant » permettant durablement aux individus d’aller vers la sphère publique., The article presents the actions carried out by a French Regional Natural Park (PNR) with inhabitants of its territory to make them aware of climate change. The very nature of climate change raises delicate strategic questions in terms of communication and public information. Among all the proceeding taken by the Park for the dissemination of scientific data developed on the local effects of climate change, the analysis relates specifically to the animation of “territorial prospective workshops” conducted with groups of residents to initiate a collective dynamic and identify the issues involving the future of the PNR geographic area.The reflection result of a dialogue between an “education” project manager and an observation researcher participating in three of the workshops.The philosophy of the workshops is based on the projection on the future articulating experiential citizen knowledge and individual knowledge on the climate, and scientific knowledge and contrasting and hypothetical scenarios of trends on the territory, in order to build a discussed, even shared vision of actions to be taken. The detour through a projection in 2070, through this co-productions of the résidents in these workshops, is experienced as a "retrospective ruse": raising awareness of the scenarios of the unacceptable, to collectively define the issues to be addressed. It has the effect for participants of positioning themselves in the present as more proactive in the future. The workshop highlights the need for institutional structures conducive to deliberation and a "learning" territory that allows individuals to move into the public sphere on a lasting basis.

Published
2021
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17. On the boundary controllability of the Korteweg–de Vries equation on a star-shaped network

Author

Claudia Moreno, Eduardo Cerpa, Emmanuelle Crépeau, Departamento de Matematica, Universidad Tecnica Federico Santa Maria, Universidad Tecnica Federico Santa Maria [Valparaiso] (UTFSM), Laboratoire de Mathématiques de Versailles (LMV), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Equations aux Dérivées Partielles (EDP), Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), and Université Paris-Saclay-Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Physics, 0209 industrial biotechnology, Control and Optimization, Applied Mathematics, 010102 general mathematics, Mathematical analysis, Boundary (topology), 02 engineering and technology, 01 natural sciences, Controllability, 020901 industrial engineering & automation, Control and Systems Engineering, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], 0101 mathematics, Korteweg–de Vries equation
Abstract

International audience; A system of N Korteweg–de Vries equations coupled by the boundary conditions is considered in this paper. The configuration studied here is the one called star-shaped network, where the boundary inputs can act on a central node and on the N external nodes. In the literature, there is a recent result proving the exact controllability of this system by using (N+1) controls. We succeed to remove the input acting on the central node and consequently we obtain the exact controllability with N inputs.

Published
2020
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18. Internal null controllability of the generalized Hirota-Satsuma system

Author

Nicolás Carreño, Eduardo Cerpa, Emmanuelle Crépeau, Departamento de Matematicas, Univesidad Tecnica Federico Santa-Maria (Valparaiso), Univesidad Federico Santa-Maria, Valparaiso, Chile, Departamento de Matematica, Universidad Tecnica Federico Santa Maria, Universidad Tecnica Federico Santa Maria [Valparaiso] (UTFSM), Equations aux Dérivées Partielles (EDP), Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), Equations aux Dérivées Partielles [2020-....] (EDP [2020-....]), Laboratoire Jean Kuntzmann [2020-....] (LJK [2020-....]), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2020-....] (UGA [2020-....])-Institut polytechnique de Grenoble - Grenoble Institute of Technology [2020-....] (Grenoble INP [2020-....]), Université Grenoble Alpes [2020-....] (UGA [2020-....])-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2020-....] (UGA [2020-....])-Institut polytechnique de Grenoble - Grenoble Institute of Technology [2020-....] (Grenoble INP [2020-....]), Université Grenoble Alpes [2020-....] (UGA [2020-....]), Laboratoire de Mathématiques de Versailles (LMV), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Equations aux Dérivées Partielles [2016-2019] (EDP [2016-2019]), Laboratoire Jean Kuntzmann [2016-2019] (LJK [2016-2019]), and Institut polytechnique de Grenoble - Grenoble Institute of Technology [2007-2019] (Grenoble INP [2007-2019])-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology [2007-2019] (Grenoble INP [2007-2019])-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])

Subjects
Inverse function theorem, 0209 industrial biotechnology, Control and Optimization, 010102 general mathematics, Linear system, Null (mathematics), Duality (optimization), 02 engineering and technology, Carleman estimates, 01 natural sciences, null controllability, Controllability, Computational Mathematics, Nonlinear system, 020901 industrial engineering & automation, Nonlinear Sciences::Exactly Solvable and Integrable Systems, Control and Systems Engineering, Bounded function, Korteweg-de Vries equation, Applied mathematics, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], 0101 mathematics, [MATH]Mathematics [math], Korteweg–de Vries equation, Mathematics
Abstract

International audience; The generalized Hirota-Satsuma system consists of three coupled nonlinear Korteweg-de Vries (KdV) equations. By using two distributed controls it is proven in this paper that the local null controllability property holds when the system is posed on a bounded interval. First, the system is linearized around the origin obtaining two decoupled subsystems of third order dispersive equations. This linear system is controlled with two inputs, which is optimal. This is done with a duality approach and some appropriate Carleman estimates. Then, by means of an inverse function theorem, the local null controllability of the nonlinear system is proven.

Published
2020
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19. Boundary controllability of the Korteweg-de Vries equation on a tree-shaped network

Author

Eduardo Cerpa, Julie Valein, Emmanuelle Crépeau, Departamento de Matematica, Universidad Tecnica Federico Santa Maria, Universidad Tecnica Federico Santa Maria [Valparaiso] (UTFSM), Equations aux Dérivées Partielles (EDP), Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA), Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization (SPHINX), Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), This work has been partially supported by FONDECYT 1180528, Math-Amsud ICoPS 17-MATH-04, and Basal Project FB0008 AC3E, ANR-16-CE40-0013,ISDEEC,Interactions entre Systèmes Dynamiques, Equations d'Evolution et Contrôle(2016), Equations aux Dérivées Partielles [2016-2019] (EDP [2016-2019]), Laboratoire Jean Kuntzmann [2016-2019] (LJK [2016-2019]), Institut polytechnique de Grenoble - Grenoble Institute of Technology [2007-2019] (Grenoble INP [2007-2019])-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology [2007-2019] (Grenoble INP [2007-2019])-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), and Basal Project FB0008 AC3E

Subjects
Coupling, Control and Optimization, Applied Mathematics, 010102 general mathematics, Mathematical analysis, MSC : 93B05, 35Q53, 35R02, Boundary (topology), 01 natural sciences, 010101 applied mathematics, Controllability, Tree shaped, Control theory, Modeling and Simulation, Boundary value problem, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], 0101 mathematics, Korteweg–de Vries equation, Mathematics
Abstract

International audience; Controllability of coupled systems is a complex issue depending on the coupling conditions and the equations themselves. Roughly speaking, the main challenge is controlling a system with less inputs than equations. In this paper this is successfully done for a system of Korteweg-de Vries equations posed on an oriented tree shaped network. The couplings and the controls appear only on boundary conditions.

Published
2019
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20. Contrôlabilité de l'équation de Boussinesq améliorée

Author

Emmanuelle Crépeau, Eduardo Cerpa, Departamento de Matematica, Universidad Tecnica Federico Santa Maria, Universidad Tecnica Federico Santa Maria [Valparaiso] (UTFSM), Laboratoire de Mathématiques de Versailles (LMV), and Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)

Subjects
0209 industrial biotechnology, Control and Optimization, Fixed-point theorem, exact controllability, 02 engineering and technology, Fixed point, 01 natural sciences, symbols.namesake, 020901 industrial engineering & automation, 0101 mathematics, Mathematics, moving control, Applied Mathematics, 010102 general mathematics, Mathematical analysis, approximate controllability, Torus, Boussinesq type equation, spectral analysis, Controllability, Moment (mathematics), Nonlinear system, Bounded function, Dirichlet boundary condition, symbols, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], moment method
Abstract

The improved Boussinesq equation is studied in this paper. Control properties for this equation posed on a bounded interval are first considered. When the control acts through the Dirichlet boundary condition the linearized system is proved to be approximately but not spectrally controllable. In a second part, the equation is posed on the one-dimensional torus and distributed moving controls are considered. Under some condition on the velocity at which the control moves, exact controllability results for both linear and nonlinear improved Boussinesq equations are obtained applying the moment method and a fixed point argument.

Published
2017

21. Two approaches for the stabilization of nonlinear KdV equation with boundary time-delay feedback

Author

Julie Valein, Emmanuelle Crépeau, Lucie Baudouin, Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Laboratoire de Mathématiques de Versailles (LMV), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization (SPHINX), Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), ANR-15-CE23-0014,SCIDIS,Stabilité et commande de systèmes de dimension infinie(2015), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), and Université de Toulouse (UT)

Subjects
Well-posed problem, Lyapunov function, 0209 industrial biotechnology, exponential stability, Boundary (topology), time-delay, 02 engineering and technology, Stability (probability), [SPI.AUTO]Engineering Sciences [physics]/Automatic, symbols.namesake, 020901 industrial engineering & automation, Mathematics - Analysis of PDEs, Exponential stability, FOS: Mathematics, Keyword: Korteweg-de Vries non-linear equation, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Observability, Electrical and Electronic Engineering, Korteweg–de Vries equation, Mathematics, Mathematical analysis, Lyapunov functional, Computer Science Applications, Nonlinear system, Control and Systems Engineering, symbols, Analysis of PDEs (math.AP)
Abstract

International audience; This article concerns the nonlinear Korteweg-de Vries equation with boundary time-delay feedback. Under appropriate assumption on the coefficients of the feedbacks (delayed or not), we first prove that this nonlinear infinite dimensional system is well-posed for small initial data. The main results of our study are two theorems stating the exponential stability of the nonlinear time delay system. Two different methods are employed: a Lyapunov functional approach (allowing to have an estimation on the decay rate, but with a restrictive assumption on the length of the spatial domain of the KdV equation) and an observability inequality approach, with a contradiction argument (for any non critical lengths but without estimation on the decay rate). Some numerical simulations are given to illustrate the results.

Published
2017
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22. Lipschitz stability in an inverse problem for the Kuramoto–Sivashinsky equation

Author

Alberto Mercado, Emmanuelle Crépeau, Lucie Baudouin, and Eduardo Cerpa

Subjects
Nonlinear system, Generalized inverse, Applied Mathematics, Inverse scattering problem, Mathematical analysis, Boundary (topology), Uniqueness, Inverse problem, Lipschitz continuity, Stability (probability), Analysis, Mathematics
Abstract

This paper presents an inverse problem for the nonlinear 1-d Kuramoto-Sivashinsky (K-S) equation. More precisely, we study the nonlinear inverse problem of retrieving the anti-diffusion coefficient from the measurements of the solution on a part of the boundary and at some positive time everywhere. Uniqueness and Lipschitz stability for this inverse problem are proven with the Bukhgeim-Klibanov method. The proof is based on a global Carleman estimate for the linearized K-S equation.

Published
2013
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23. Semi-classical signal analysis

Author

Michel Sorine, Taous-Meriem Laleg-Kirati, Emmanuelle Crépeau, Estimation Modelling and ANalysis Group (KAUST-CEMSE), King Abdullah University of Science and Technology (KAUST), Laboratoire de Mathématiques de Versailles (LMV), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), SIgnals and SYstems in PHysiology & Engineering (SISYPHE), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Advanced 3D Numerical Modeling in Geophysics (Magique 3D), Laboratoire de Mathématiques et de leurs Applications [Pau] (LMAP), and Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)-Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest

Subjects
Control and Optimization, [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], FOS: Physical sciences, 02 engineering and technology, 01 natural sciences, Signal, Discrete spectrum, symbols.namesake, [SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph], 0202 electrical engineering, electronic engineering, information engineering, Waveform, 0101 mathematics, Mathematical Physics, Mathematics, Schrödinger operator, Signal processing, Applied Mathematics, Operator (physics), 010102 general mathematics, Mathematical analysis, 020206 networking & telecommunications, Mathematical Physics (math-ph), [INFO.INFO-NA]Computer Science [cs]/Numerical Analysis [cs.NA], Signal analysis, Control and Systems Engineering, Signal Processing, symbols, Arterial blood pressure, Semi-classical, [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing, Schrödinger's cat
Abstract

International audience; This study introduces a new signal analysis method, based on a semiclassical approach. The main idea in this method is to interpret a pulse-shaped signal as a potential of a Schrödinger operator and then to use the discrete spectrum of this operator for the analysis of the signal. We present some numerical examples and the first results obtained with this method on the analysis of arterial blood pressure waveforms.

Published
2012
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24. Rapid exponential stabilization for a linear Korteweg-de Vries equation

Author

Eduardo Cerpa and Emmanuelle Crépeau

Subjects
Forcing (recursion theory), Applied Mathematics, Mathematical analysis, Zero (complex analysis), Boundary (topology), Controllability, symbols.namesake, Exponential growth, Control system, Dirichlet boundary condition, symbols, Discrete Mathematics and Combinatorics, Korteweg–de Vries equation, Mathematics
Abstract

We consider a control system for a Korteweg-de Vries equation with homogeneous Dirichlet boundary conditions and Neumann boundary control. We address the rapid exponential stabilization problem. More precisely, we build some feedback laws forcing the solutions of the closed-loop system to decay exponentially to zero with arbitrarily prescribed decay rates. We also perform some numerical computations in order to illustrate this theoretical result.

Published
2009
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25. Approximate controllability of a reaction-diffusion system

Author

Christophe Prieur, Emmanuelle Crépeau, Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT), Laboratoire de Mathématiques de Versailles (LMV), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National Polytechnique (Toulouse) (Toulouse INP), and Université Fédérale Toulouse Midi-Pyrénées

Subjects
General Computer Science, Series (mathematics), Differential equation, Mechanical Engineering, Flatness (systems theory), 010102 general mathematics, Mathematical analysis, Motion control, 01 natural sciences, 010101 applied mathematics, Controllability, Control and Systems Engineering, Ordinary differential equation, MSC : 93B05 (93C20), Reaction–diffusion system, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], 0101 mathematics, Electrical and Electronic Engineering, ComputingMilieux_MISCELLANEOUS, Mathematics
Abstract

An open-loop control for a system coupling a reaction-diffusion system and an ordinary differential equation is proposed in this study. We use a flatness-like property, indeed, the solution can be expressed in terms of an infinite series depending on a flat output, its derivatives and its integrals. This series is shown to be convergent if the flat output is Gevrey of order 1 a ≤ 2 . Approximate controllability of the system is then proved.

Published
2008
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26. Parsimonious Representation of Signals Based on Scattering Transform

Author

Qinghua Zhang, Taous-Meriem Laleg, Emmanuelle Crépeau, Michel Sorine, SIgnals and SYstems in PHysiology & Engineering (SISYPHE), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Laboratoire de Mathématiques de Versailles (LMV), and Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)

Subjects
0209 industrial biotechnology, Mathematical optimization, Signal processing, Inverse scattering transform, 010102 general mathematics, Feature extraction, 02 engineering and technology, General Medicine, Eigenfunction, 01 natural sciences, 020901 industrial engineering & automation, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, 0101 mathematics, Representation (mathematics), Algorithm, Eigenvalues and eigenvectors, Data compression, Mathematics, Interpolation
Abstract

International audience; A parsimonious representation of signals is a mathematic model parametrized with a small number of parameters. Such models are useful for analysis, interpolation, filtering, feature extraction, and data compression. A new parsimonious model is presented in this paper based on scattering transforms. It is closely related to the eigenvalues and eigenfunctions of the linear Schrödinger equation. The efficiency of this method is illustrated in this paper with examples of both synthetic and real signals.

Published
2008
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27. Control of a clamped-free beam by a piezoelectric actuator

Author

Christophe Prieur and Emmanuelle Crépeau

Subjects
Control and Optimization, Diophantine equation, Mathematical analysis, Boundary (topology), Space (mathematics), Computer Science::Other, Controllability, Computational Mathematics, Control and Systems Engineering, Control theory, Piezoelectric actuators, Uniqueness, Actuator, Beam (structure), Mathematics
Abstract

We consider a controllability problem for a beam, clamped at one boundary and free at the other boundary, with an attached piezoelectric actuator. By Hilbert Uniqueness Method (HUM) and new results on diophantine approximations, we prove that the space of exactly initial controllable data depends on the location of the actuator. We also illustrate these results with numerical simulations.

Published
2006
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28. Exact boundary controllability of a nonlinear KdV equation with critical lengths

Author

Emmanuelle Crépeau and Jean-Michel Coron

Subjects
0209 industrial biotechnology, Applied Mathematics, General Mathematics, 010102 general mathematics, Mathematical analysis, Mathematics::Analysis of PDEs, Boundary (topology), 02 engineering and technology, Interval (mathematics), 01 natural sciences, Term (time), Controllability, symbols.namesake, Nonlinear system, Nonlinear Sciences::Exactly Solvable and Integrable Systems, 020901 industrial engineering & automation, Linearization, Dirichlet boundary condition, symbols, 0101 mathematics, Korteweg–de Vries equation, Mathematics
Abstract

We study the boundary controllability of a nonlinear Korteweg-de Vries equation with the Dirichlet boundary condition on an interval with a critical length for which it has been shown by Rosier that the linearized control system around the origin is not controllable. We prove that the nonlinear term gives the local controllability around the origin.

Published
2004
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29. Exact boundary controllability of the Korteweg?de Vries equation around a non-trivial stationary solution

Author

Emmanuelle CrÉpeau

Subjects
Vries equation, Controllability, Nonlinear Sciences::Exactly Solvable and Integrable Systems, Control and Systems Engineering, Bounded function, Mathematical analysis, Boundary (topology), Derivative, Korteweg–de Vries equation, Stationary solution, Domain (mathematical analysis), Computer Science Applications, Mathematics
Abstract

The exact boundary controllability of the non-linear Korteweg-de Vries equation on bounded domains is studied. Only the first spatial derivative at the right endpoint is assumed to be controlled. In this case, the exact controllability has been shown by Rosier (1997) when the length L of the domain is not in the set N

Published
2001
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30. Discussion on: 'Adaptive Boundary Control of the Forced Generalized Korteweg-de Vries-Burgers Equation'

Author

Christophe Prieur, Emmanuelle Crépeau, Laboratoire de Mathématiques de Versailles (LMV), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées, Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), and Université de Toulouse (UT)

Subjects
0209 industrial biotechnology, 010102 general mathematics, Mathematical analysis, General Engineering, Boundary (topology), 02 engineering and technology, Mixed boundary condition, 01 natural sciences, Burgers' equation, 020901 industrial engineering & automation, MSC : 93C20 (35Q53 65M60 93B40 93D21), [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], 0101 mathematics, Control (linguistics), ComputingMilieux_MISCELLANEOUS, Mathematics
Abstract

International audience

Published
2010
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31. On the determination of the principal coefficient from boundary measurements in a KdV equation

Author

Eduardo Cerpa, Alberto Mercado, Emmanuelle Crépeau, and Lucie Baudouin

Subjects
Nonlinear Sciences::Exactly Solvable and Integrable Systems, Applied Mathematics, Mathematical analysis, Inverse scattering problem, Principal (computer security), Mathematics::Analysis of PDEs, Boundary (topology), Inverse problem, Lipschitz continuity, Korteweg–de Vries equation, Nonlinear Sciences::Pattern Formation and Solitons, Stability (probability), Mathematics
Abstract

This paper concerns the inverse problem of retrieving the principal coefficient in a Korteweg–de Vries (KdV) equation from boundary measurements of a single solution. The Lipschitz stability of this inverse problem is obtained using a new global Carleman estimate for the linearized KdV equation. The proof is based on the Bukhgeĭm–Klibanov method.

Published
2014

32. Global Carleman estimate on a network for the wave equation and application to an inverse problem

Author

Lucie Baudouin, Julie Valein, Emmanuelle Crépeau, Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Laboratoire de Mathématiques de Versailles (LMV), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Robust control of infinite dimensional systems and applications (CORIDA), Institut Élie Cartan de Nancy (IECN), Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Lorraine (INPL)-Université Nancy 2-Université Henri Poincaré - Nancy 1 (UHP)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Lorraine (INPL)-Université Nancy 2-Université Henri Poincaré - Nancy 1 (UHP)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de Mathématiques et Applications de Metz (LMAM), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria), Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Lorraine (INPL)-Université Nancy 2-Université Henri Poincaré - Nancy 1 (UHP)-Institut National de Recherche en Informatique et en Automatique (Inria), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire de Mathématiques et Applications de Metz (LMAM), and Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Control and Optimization, Applied Mathematics, 010102 general mathematics, Mathematical analysis, Stability (learning theory), Boundary (topology), Inverse problem, Carleman estimate, Lipschitz continuity, Wave equation, 01 natural sciences, 010101 applied mathematics, AMS : 35R30, 93C20, Inverse scattering problem, C++ string handling, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], 0101 mathematics, Networks, Mathematics
Abstract

20 pages; International audience; We are interested in an inverse problem for the wave equation with potential on a starshaped network. We prove the Lipschitz stability of the inverse problem consisting in the determination of the potential on each string of the network with Neumann boundary measurements at all but one external vertices. Our main tool, proved in this article, is a global Carleman estimate for the network.

Published
2011
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33. Boundary controllability for the nonlinear Korteweg-de Vries equation on any critical domain

Author

Eduardo Cerpa, Emmanuelle Crépeau, Laboratoire de Mathématiques d'Orsay (LM-Orsay), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), Laboratoire de Mathématiques de Versailles (LMV), and Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)

Subjects
0209 industrial biotechnology, Mathematics::Analysis of PDEs, Boundary (topology), 02 engineering and technology, 01 natural sciences, Dispersionless equation, symbols.namesake, 020901 industrial engineering & automation, Boundary value problem, 0101 mathematics, Korteweg–de Vries equation, Nonlinear Sciences::Pattern Formation and Solitons, Mathematical Physics, ComputingMilieux_MISCELLANEOUS, Mathematics, MSC : 93B05 (35Q53 76B75 93C20), Applied Mathematics, 010102 general mathematics, Mathematical analysis, Nonlinear system, Nonlinear Sciences::Exactly Solvable and Integrable Systems, Dirichlet boundary condition, symbols, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Series expansion, Analysis, Linear equation
Abstract

It is known that the linear Korteweg–de Vries (KdV) equation with homogeneous Dirichlet boundary conditions and Neumann boundary control is not controllable for some critical spatial domains. In this paper, we prove in these critical cases, that the nonlinear KdV equation is locally controllable around the origin provided that the time of control is large enough. It is done by performing a power series expansion of the solution and studying the cascade system resulting of this expansion.

Published
2009
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34. Arterial blood pressure analysis based on scattering transform I

Author

Michel Sorine, Yves Papelier, Taous-Meriem Laleg, Emmanuelle Crépeau, Applications and Tools of Automatic Control (SOSSO2), Inria Paris-Rocquencourt, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)

Subjects
Quantitative Biology::Tissues and Organs, 0206 medical engineering, Physics::Medical Physics, [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], schrödinger operator, Blood Pressure, 02 engineering and technology, 01 natural sciences, signal analysis, Schrödinger equation, symbols.namesake, [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, [SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph], solitons, Humans, Computer Simulation, Diagnosis, Computer-Assisted, 0101 mathematics, Eigenvalues and eigenvectors, Mathematics, Signal processing, Scattering, Operator (physics), 010102 general mathematics, Mathematical analysis, Models, Cardiovascular, arterial blood pressure, Blood Pressure Determination, Arteries, 020601 biomedical engineering, Scattering transform, Blood pressure, Fourier transform, Flow (mathematics), symbols, [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing, Algorithms, Blood Flow Velocity, [MATH.MATH-SP]Mathematics [math]/Spectral Theory [math.SP]
Abstract

This article presents a new method for analyzing arterial blood pressure waves. The technique is based on the scattering transform and consists in solving the spectral problem associated to a one-dimensional Schrödinger operator with a potential depending linearly upon the pressure. This potential is then expressed with the discrete spectrum which includes negative eigenvalues and corresponds to the interacting components of an N-soliton. The approach is analogous to the Fourier transform where the solitons play the role of sinus and cosinus components. The proposed method seems to have interesting clinical applications. It can be used for example to separate the fast and slow parts of the blood pressure that correspond to the systolic (pulse transit time) and diastolic phases (low velocity flow) respectively.

Published
2007

35. Travelling-wave analysis and identification. A scattering theory framework

Author

Michel Sorine, Emmanuelle Crépeau, Taous-Meriem Laleg, Applications and Tools of Automatic Control (SOSSO2), Inria Paris-Rocquencourt, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)

Subjects
0206 medical engineering, 010103 numerical & computational mathematics, 02 engineering and technology, 01 natural sciences, Solitons, Standing wave, symbols.namesake, arterial blood pressure, [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, [SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, 0101 mathematics, Mathematics, scattering theory, Operator (physics), Mathematical analysis, 020601 biomedical engineering, Isospectral, Classical mechanics, Flow (mathematics), Fourier analysis, Inverse scattering problem, symbols, identification, schrodinger operator, Scattering theory, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing, Schrödinger's cat
Abstract

This article presents a new travelling waves analysis and identification method based on scattering theory. This inverse scattering technique consists in solving the spectral problem associated to a one-dimensional Schrodinger operator perturbed by a potential depending upon the wave to analyze, and optimized in order to approximate this wave by an isospectral flow in the sense of Lax. In this method, the interacting components of an N-soliton are the elementary travelling waves for the approximation. These N solitons play an analogous role to linear superpositions of sinus and cosinus in the Fourier analysis of standing waves. In the proposed analysis of travelling waves, low and high frequency components are replaced by low and high velocity components. Two applications of the method are presented. The first one concerns the identification of an N-soliton and is illustrated with N = 3. The second one consists in the analysis of the arterial blood pressure waves during the systolic phase (pulse transit time) and the diastolic phase (low velocity flow).

Published
2007

36. Identifiability of a reduced model of pulsatile flow in an arterial compartment

Author

Michel Sorine and Emmanuelle Crépeau

Subjects
Nonlinear system, Singular perturbation, Flow (mathematics), Wave propagation, Mathematical analysis, Dispersion (water waves), Korteweg–de Vries equation, Navier–Stokes equations, Transfer function, Mathematics
Abstract

In this article we propose a reduced model of the input-output behaviour of an arterial compartment, including the short systolic phase where wave phenomena are predominant. The objective is to provide basis for model-based signal processing methods for the estimation from non-invasive measurements and the interpretation of the characteristics of these waves. Standard space discretizations of distributed models of the flow lead to high order models for the pressure wave transfer function, and low order rational transfer functions approximations give poor results. The main idea developed here to circumvent these problems is to explicitly use a propagation delay in the reduced model. Due to phenomena such that peaking and steepening, the considered pressure pulse waves behave more like solitons generated by a Korteweg de Vries (KdV) equation than like linear waves. So we start with a quasi-1D Navier-Stokes equation that takes into account a radial acceleration of the wall, in order to be able to recover, during the reduction process, the dispersive term of KdV equation which, combined with the nonlinear transport term gives rise to solitons. The radial and axial acceleration terms being supposed small, a multiscale singular perturbation technique is used to separate the fast wave propagation phenomena taking place in a boundary layer in time and space described by a KdV equation from the slow phenomena represented by a parabolic equation leading to two-elements windkessel models.

Published
2006
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37. Separation of arterial pressure into solitary waves and windkessel flow

Author

Michel Sorine, Emmanuelle Crépeau, Taous-Meriem Laleg, Applications and Tools of Automatic Control (SOSSO2), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Laboratoire de Mathématiques de Versailles (LMV), and Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)

Subjects
Signal processing, [SDV.OT]Life Sciences [q-bio]/Other [q-bio.OT], 0206 medical engineering, Linear system, Mathematical analysis, 02 engineering and technology, wave, identifiability, 020601 biomedical engineering, 2-element windkessel, Pulse (physics), 03 medical and health sciences, Superposition principle, pressure, 0302 clinical medicine, Airy wave theory, Flow (mathematics), solitons, Identifiability, Soliton, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], 030217 neurology & neurosurgery, Mathematics
Abstract

International audience; A simplified model of arterial blood pressure intended for use in model-based signal processing applications is presented. The main idea is to decompose the pressure into two components: a travelling wave describes the fast propagation phenomena predominating during the systolic phase and a windkessel flow represents the slow phenomena during the diastolic phase. Instead of decomposing the blood pressure pulse into a linear superposition of forward and backward harmonic waves, as in the linear wave theory, a nonlinear superposition of travelling waves matched to a reduced physical model of the pressure, is proposed. Very satisfactory experimental results are obtained by using forward waves, the N- soliton solutions of a Korteweg-de Vries equation in conjunction with a two-element windkessel model. The parameter identifiability in the practically important 3- soliton case is also studied. The proposed approach is briefly compared with the linear one and its possible clinical relevance is discussed.

Published
2006

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