- Operatorial transformations of dynamic problems
- Operatorial parametrization of dynamic systems
- Analysis and simulation of non local dynamic models
- Nonlinear control and identification
Journal Publications (6) (expand/reduce)
- System Identification by Operatorial Cancellation of Nonlinear Terms and Application to a Class of Volterra Models
C. Casenave, E. Montseny, G. Montseny
International Journal of Robust and Nonlinear Control, Volume 27, Issue 8, pages 1211–1241, 25th of may 2017.Abstract: In this paper, a method is proposed for identification of some complex SISO nonlinear models with two ill-known components of different nature: a linear (possibly dynamic) part and a static nonlinear one. This method is well adapted when no a priori information is available about the nonlinear component to be identified. It is based on a difference operator which enables to cancel the nonlinear terms when applied to the model. Only the ill-known linear part remains in the transformed model: it can therefore be identified independently of the nonlinear term. The problems under consideration are defined in an abstract framework, with very weak hypotheses, so that the proposed approach has a large scope. To highlight the method, a class of dynamic Volterra models including some hybrid models such as dynamic inclusions is considered for application.
Keywords: System identification, Operatorial cancellation, Nonlinear system, Volterra model, Diffusive representation
- Analysis, simulation and impedance operator of a non local model of porous medium for acoustic control.
E. Montseny and C. Casenave
Journal of Vibration and Control April 2015 21: 1012-1028, first published online on July 19, 2013.Abstract: The problem under consideration relates to a model of a porous wall devoted to aircraft motor noise reduction. For such a medium, the parameters of the propagation equation depend on the frequency. Then, the corresponding time-model involves non rational convolution operators, which make the model complex from both the analysis and the simulation point of view. In this paper, based on the so-called diffusive representation of convolution operators, a time-local formulation of the porous wall model, well adapted to analysis and numerical simulation, is established and analyzed. Then its associated impedance operator is computed. Finally some numerical results relating to the simulation of the porous wall and to the one of its impedance operator are given to highlight the theoretical part.
Keywords: porous medium, nonlocal operator, dffusive representation, impedance operator, dissipativity, acoustics.
- Identification of Nonlinear Dynamic Models of Electrostatically Actuated MEMS
C. Casenave, E. Montseny, H. Camon
Control Engineering Practice, Vol.18, N°8, pp.954-969, 2010.Abstract: This paper focuses on the identification of nonlinear dynamic models for physical systems such as electrostatically actuated Micro-Electro-Mechanical Systems (MEMS). The proposed approach consists in transforming, by means of suitable global operations, the input-output differential model in such a way that the new equivalent formulation is well adapted to the identification problem, thanks to the following properties: first, the linearity with respect to the parameters to be identified is reserved, second, the continuous dependence on noise measurements is restored. Consequently, a simple leastsquare resolution can be used, in such a way that some of the difficulties classically encountered with identification methods are by-passed. The method is implemented on real measurement data from a physical system.
Keywords: Dynamic Models; Parameters Identification; Least-squares Identification; Time-continuous identification; Electrostatically actuated Micro-Electro-Mechanical Systems
- Dissipative terms and local time-stepping improvements in a spatial high order Discontinuous Galerkin scheme for the time-domain Maxwell's equations
E. Montseny, S. Pernet, X. Ferrières, G. Cohen
Journal of Computational Physics, Vol.227, N°14, pp.6795-6820, 2008.Abstract: In this paper, we present some improvements, in terms of accuracy and speed-up, for a particular well adapted Discontinuous Galerkin method devoted to the timedomain Maxwell equations. First, to reduce spurious modes on very distorted meshes, the addition of dissipative terms as penalization in the numerical scheme is studied and compared on examples. Second, in order to increase the efficiency of the method, a multi-class local time-stepping strategy is presented and its validation and advantages are highlighted on different examples.
Keywords: Maxwell's equations, Discontinuous Galerkin method, local time-stepping
- Time-local dissipative formulation and stable numerical schemes for a class of integrodifferential wave equations
C. Casenave, E. Montseny
SIAM Journal on Applied Mathematics, Vol.68, N°6, pp.1763-1783, 2008.Abstract: We consider integrodifferential equations of the abstract form H(∂t)Φ = G(∇)Φ+f, where H(∂t) is a diagonal convolution operator and G(∇) is a linear anti-selfadjoint differential operator. On the basis of an original approach devoted to integral causal operators, we propose and study a time-local augmented formulation under the form of a Cauchy problem ∂tΨ = AΨ+Bf such that Φ = CΨ. We show that under a suitable hypothesis on the symbol H(p), this new formulation is dissipative in the sense of a natural energy functional. We then establish the stability of numerical schemes built from this time-local formulation, thanks to the dissipation of appropriate discrete energies. Finally, the efficiency of these schemes is highlighted by concrete numerical results relating to a model recently proposed for 1D acoustic waves in porous media.
Keywords: integrodifferential wave equation, partial differential equation, convolution operator, diffusive representation, numerical scheme, Cauchy problem, energy functional, stability condition
- Formulation différentielle dissipative d'un modèle de paroi absorbante en aéroacoustique
C. Casenave, E. Montseny, L. Ségui
Comptes rendus de l'Académie des Sciences - Mécanique, Vol.336, N°4, pp.398-403, 2008.Abstract: The problem under consideration relates to a particular model of porous wall devoted to aircraft motor noise reduction. Because parameters of the propagation equation are frequency dependent, the time-model of such a medium involves convolution operators. We introduce a new formulation of these operators based on their symbols, both time-local and dissipative. The coupling of this so-obtained model with a standard aeroacoustic one then leads to a time-local system whose analysis is simplified thanks to the existence of an energy functional in the sense of which the global dissipativity is insured.
Keywords: Porous media, Aircraft noise reduction, Aeroacoustics, Frequency model, Convolution operators
- Simplification of dynamic problems by time-scale transformation: application to the nonlinear control with input positive constraints.
C. Casenave, E. Montseny
20th IFAC World Congress, Toulouse (France), July 9-14th, 2017.Abstract: In this paper, we show how time-scale transformations (TST) can be used for thecontrol of nonlinear sytems subject to positive constraints. Such transformations, which consistin a change of the time variable, enable to define a new time-scale denoted \tau in which the controlproblem becomes unconstrained and is therefore simplified. Classical methods such as dynamicfeedback linearizing control design can then be used, leading to control laws that naturally fullfillthe input positive constraints. The proposed method is applied on two concrete examples andcompared with an other approach
Keywords: input positive constraints; input saturation; nonlinear control; time-scale transformation
- Control of fed-batch bioreactors models by means of dynamic time-scale transformation and operatorial parametrization
E. Montseny
18th IFAC World Congress, Milan (Italy), Aug 28-Sept 02, 2011.Abstract: In this paper, we show how operatorial transformations, defined in the trajectorial sense, can be used to significantly simplify the problem of control of fed-batch bioreactors. We first define the suitable mathematical framework and study remarkable transformations. We also introduce the notion of operatorial parametrizing and apply these notions to the control of fed-batch bioreactors models.
Keywords: Operatorial transformation, Fed-batch Bioreactor, Operatorial Parametrizing, Time Scale Transformation, Nonlinear Control.
- Desingularization of non local dynamic models by means of operatorial transformations and application to a flame model
E. Montseny
4th IFAC Symposium on System, Structure and Control, IFAC SSSC 2010, Ancona (Italy), 15-17 September 2010Abstract: In this paper, we show how suitable operatorial transformations can be used to simplify non local singular dynamic models. First, some basic notions on trajectories, operators and dynamic problems are introduced. Second, the diffusive transformation of non local models is briefly exposed. Then, time-scale transformations are introduced and some essentials properties are stated; the desingularization of models (in general non time local) is then studied. Finally, those transformations are applied on a singular implicit and non local flame model.
- Simple and Efficient Control of MEMS by Means of Operatorial Model Transformations
E. Montseny, H. Camon
SYMPOSIUM on Design, Test, Integration & Packaging of MEMS/MOEMS, DTIP 2010, Seville (Spain), 5-7 May 2010Abstract: We present a simple and original method well suited for designing efficient control strategies of any type, for a generic class of MEMS. This method is particularly well adapted when high performances and precision are required, because it is intensively based on the predictive capabilities of the model without needing its resolution, which make the method both simple to implement and robust.
Keywords: MEMS, nonlinear control, operatorial transformations, time-scale transforamtion, parametrization
- Identification of Electrostatically Actuated MEMS Models from Real Measurement Data
C. Casenave, E. Montseny, H. Camon
15th IFAC Symposium on System Identification, SYSID 2009, Saint-Malo (France), July 6-8 2009.Abstract: This paper focuses on the identification of nonlinear dynamic models for physical systems such as Micro-Electro-Mechanical Systems (MEMS) from measurement data. The proposed approach consists in transforming, by means of suitable global operations, the specific input-output differential physical model of the system elaborated from physical analysis, in such a way that we get a new equivalent model formulation specifically adapted to the identification problem. Thanks to the equivalence of the dynamic model and the derived identification problem, the so-identified model remains of continuous-time type, with a clear physical meaning of any of its component, which is not the case when using, for example, black-boxes approaches. The method is implemented on real measurement data from a physical system.
Keywords: Dynamic models, parameters identification, nonlinear models, least-squares identification, MEMS, micromirror
- Operatorial parametrizing of controlled dynamic systems. Application to the fed-batch bioreactor control problem
E.Montseny, A. Doncescu
17th IFAC World Congress, Seoul (Korea), July 6-11, 2008, pp.7486-7490.Abstract: Dynamic models most of time involve differential equations, which are 'time-local'. Such models can also be considered 'globally', that is in the sense of 'trajectories' in the state 'space-time'. Up to adapted concepts, such a different interpretation reveals itself more flexible, namely because it allows to use various operatorial transformations whose time-local equivalent in general cannot exist and from which can result some remarkable properties. Namely, we introduce a principle of parametrizing for dynamic equations by means of such transformations. We then consider an example of bioreactor model for which we highlight how suitable timenonlocal transformations can sometimes be used to efficiently solve some nonlinear control problems.
Keywords: Dynamic system, Parametrizing, Operator, Time Scale Transformation, Control, Fed-batch Bioreactor
- Dissipative state formulations and numerical simulation of a porous medium for boundary absorbing control of aeroacoustic waves
C. Casenave, E. Montseny
17th IFAC World Congress, Seoul (Korea), July 6-11, 2008, pp.13432-13437.Abstract: The problem under consideration relates to a model of porous wall devoted to aircraft motors noise reduction. For such a medium, the parameters of the propagation equation depend on the frequency, so the corresponding time-model involves non rational convolution operators. Consequently, the impedance of the wall is a non rational function of the frequency. On the basis of complex analysis and causality properties, we introduce infinite dimensional state formulations of these operators. The coupling of the so-obtained model with a standard aeroacoustic one then leads to a time-local system whose analysis is simplified thanks to the existence of an energy functional in the sense of which the global dissipativity is insured. Some numerical results are given to illustrate the theoretical results.
- Reduction of complexity via operatorial parametric formulations for some nonlinear dynamic problems of biology
E. Montseny, A. Doncescu
IEEE International Symposium on Bioinformatics and Life Science Modeling and Computing (BLSMC08), Okinawa (Japan), March 25-28, 2008.Abstract: Dynamic models most of the time involve differential equations, which are 'time-local'. Such models can also be considered 'globally', that is in the sense of trajectories in the 'space-time' state. Up to adapted concepts, such a different interpretation reveals itself more flexible, namely because it allows to use various operatorial transformations whose time-local equivalent in general cannot exist and from which can result some remarkable properties. Namely, we introduce a principle of parametrizing for dynamic equations by means of such transformations. We then consider an example of bioreactor model for which we highlight how suitable time-nonlocal transformations can sometimes be used to efficiently solve some nonlinear control problems.
- A discontinuous galerkin method to solve maxwell equations in time domain
E. Montseny, S. Pernet, X. Ferrières, M. Zweers, G. Cohen, B. Becqueux
23rd International Review of Progress in Applied Computational Electromagnetics (ACES 2007), Verone (Italy), March 19-23, 2007.Abstract: In this paper, we describe a high-order spatial Discontinuous Galerkin approach to solve Maxwell's equations in the time domain. This approach is based on the use of hexahedral meshes and on a judicious choice for the approximations spaces. This results in an efficient solver in terms of storage and CPU time, for any order of approximation.
- Méthodes de pas de temps local appliquées à un schéma Galerkin discontinu pour résoudre les équations de Maxwell 3D dans le domaine temporel
E. Montseny, X. Ferrières
5ème Conférence Européenne sur les Méthodes Numériques en Electromagnétisme (NUMELEC'06), Lille (France), Nov 29 - 1st of Dec, 2006, pp.59-60.Abstract: L'étude de champs au voisinage de parois nécessite un maillage spatialement raffiné et l'utilisation de méthodes de type Galerkin discontinu d'ordre élevé. Un maillage raffiné implique cependant un pas de temps global très petit et donc une perte d'efficacité du schéma numérique. On présente dans ce papier la méthode de Galerkin considérée et certaines stratégies de pas de temps local que l'on peut envisager, tout en mettant en évidence leurs limites.
Keywords: Galerkin discontinu, pas de temps local, raffinement de maillage, leap-frog récursif
- Etude préliminaire d'une loi de régulation-poursuite à faible gain pour référence de tension de haute précision à base de MEMS (rapport intermédiaire)
Montseny, G. and Casenave, C. and Montseny, E. and Camon, H. and Blard, F.
Convention LAAS-LNE 2008, Modélisation et identification du comportement de structures MEMS pour l'élaboration d'une loi de commande appliquée à l'électronique basée sur la tension de pull-inAbstract:
- Modélisation, identification et validation (rapport intermédiaire)
Casenave, C. and Montseny, E. and Camon, H.
Convention LAAS-LNE 2008, Modélisation et identification du comportement de structures MEMS pour l'élaboration d'une loi de commande appliquée à l'électronique basée sur la tension de pull-inAbstract:
- Transformations opératorielles de problèmes dynamiques et applications
E. Montseny
PhD Thesis in Automatics, 2009.
Abstract:De manière générale, l'automatique est une science consistant à résoudre des problèmes définis sur des modèles dynamiques, c'est-à-dire des modèles d'évolution. Pendant longtemps, les moyens de calculs limités ont empêché l'essor d'opérations complexes et favorisé les analyses essentiellement centrées sur la notion d'espace d'état et de systèmes différentiels. Pour les systèmes linéaires, la transformation de Laplace est un outil de base, permettant de transformer une équation différentielle en équation algébrique résoluble avec peu de calculs. Pour les systèmes non linéaires, de nombreuses approches ont permis et permettent de résoudre divers problèmes de manière satisfaisante et peu coûteuse.
Cependant, nombreux sont les problèmes nécessitant d'être posés de manière globale, dans un espace de trajectoire. Tel est le cas, par exemple, des modèles intégrodifférentiels (ou "non locaux en temps") qui imposent, de par leur formulation même, une analyse et une résolution "trajectorielles", au moyen d'opérateurs, c'est-à-dire de fonctions de trajectoires, là où les modèles différentiels n'exigent que des fonctions. A condition de restreindre les opérations à des classes "raisonnables", les moyens de calcul actuels permettent d'envisager le traitement de nombreux problèmes en travaillant globalement sur les trajectoires d'évolution. En particulier, excepté dans certains cas particuliers dont la complexité reste encore pénalisante, on peut considérer que les opérateurs issus de l'intégration de modèles différentiels linéaires sont relativement peu coûteux, tant au niveau théorique que numérique. Et, de même que les transformations "locales" permettent dans nombre de cas de reformuler un problème sous une forme mieux adaptée à l'analyse ou à la résolution numérique, des "transformations opératorielles", plus riches car définies par des opérateurs agissant sur des espaces de trajectoires (et dont les transformations locales font partie), sont susceptibles d'apporter des simplification plus significatives encore, sous réserve que l'on puisse mettre en oeuvre les solutions auxquelles elles conduisent. Dans cette optique, la notion d'opérateur sur des trajectoire nécessite l'utilisation d'outils mathématiques adaptés: analyse fonctionnelle, topologie, etc. afin de garantir, notamment, la continuité des transformations en adaptant les topologies des espaces de trajectoires sur lesquels ont travaille. Il s'agit là d'une richesse que n'offrent pas les espaces d'état de dimension finie de type Rn classiquement utilisés.
L'objet de cette thèse est de formaliser et étudier la problématique de "transformation opératorielle" pour des problèmes dynamiques généraux, dans l'objectif d'apporter des simplifications ou améliorations significatives à l'analyse, la simulation, l'identification, la commande, l'estimation, etc., et de mettre en lumière l'intérêt de cette approche "trajectorielle" des problèmes dynamiques au moyen de quelques exemples non triviaux, traités par voie analytique et mis en oeuvre numériquement.
Keywords: transformations opératorielles, modèles non locaux, problèmes dynamiques, paramétrisation opératorielle, changement de temps, transformation diffusive, contrôle non linéaire, analyse de modèles singuliers, thèse, PhD Thesis.
Internship and projects (expand/reduce)
- Etude de méthodes de pas de temps local dans un schéma Galerkin Discontinu d'ordre élevé pour résoudre les équations de Maxwell 3D dans le domaine temporel
- Simulation de perturbations aéroacoustiques dans un guide d'ondes et mise en oeuvre de PML et CPML 2D pour l'aéroacoustique