Page UMA de Frédéric Jean
Dir. UMA
Professeur
Activités de recherche
Depuis mon doctorat de Mathématiques à l'Université Pierre et Marie Curie (Paris 6), en 1998, je suis enseignant-chercheur dans le groupe Optimisation et Commande de l'Unité de Mathématiques Appliquées (UMA) de l'ENSTA. Je suis actuellement directeur de l'UMA.
Mes activités de recherche s'inscrivent dans le contexte de la théorie du contrôle non-linéaire, et plus précisément du contrôle géométrique: l'objectif est d'aborder par des méthodes de la géométrie différentielle les questions type de l'automatique et la théorie du contrôle. Mes recherches portent d'une part sur des aspects théoriques: géométrie sous-riemannienne, systèmes non-holonomes, approche géométrique du contrôle optimal; et d'autre part sur la modélisation de la neuro-physiologie au moyen de système commandés, plus particulièrement sur l'identification de principes de minimisations (problèmes de contrôle optimal inverse).
Encadrement doctoral:
- Ruixing Long (co-encadrement avec Yacine Chitour), thèse soutenue en 2010;
- Dario Prandi (co-encadrement avec Ugo Boscain et Mario Sigalotti), thèse soutenue en 2013;
- Cristopher Hermosilla (co-encadrement avec Hasnaa Zidani), thèse soutenue en 2015;
- Boutheina Hafassa (co-encadrement avec Yacine Chitour, Mario Sigalotti), thèse soutenue en 2016;
- Walid Bouhafs (co-encadrement avec Nahla Abdellatif), thèse soutenue en 2016;
- Sofya Maslovskaya (co-encadrement avec Igor Zelenko), thèse soutenue en 2018;
- Emilien Flayac (co-encadrement avec Karim Dahia et Bruno Hérissé), thèse soutenue en 2019;
- Meryem Kafnemer (co-encadrement avec Yacine Chitour), thèse soutenue en 2022;
- Othmane Jerhaoui (co-encadrement avec Hasnaa Zidani), thèse soutenue en 2022;
- Clara Leparoux (co-encadrement avec Bruno Hérissé), thèse soutenue en 2023;
- En Lai (co-encadrement avec Antoine Girard et Riccardo Bonalli), thèse débutée en 2024.
Activités d'enseignement
Enseignements à l'ENSTA:
- le cours APM_3AOT3 (ex AOT13)- Géométrie différentielle appliquée;
- le cours APM_3AO02 (ex AO102) - Systèmes Dynamiques: Analyse et Stabilité;
- le cours APM_4AUT1 (ex AUT201) - Commande des systèmes.
Cours de M2 (jusqu'en 2020):
- le cours Geometric Control, avec U. Boscain et Y. Chitour, M2 Optimisation de l'Université Paris-Saclay (2015-2020);
- le cours Planification de mouvements, avec H. Zidani, M2 ATSI de l'Université Paris-Saclay; ce cours fait également partie de la 3ème année de l'ENSTA, sous le sigle OROC-SC-PL (2015-2020).
Autres activités
Publications
Articles (revues avec comité de lecture)
Soumis
- A unifying vision of Particle Filtering and Explicit Dual Control
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soumis - Co-Contraction Embodies Uncertainty: An Optimal Feedforward Strategy for Robust Motor Control
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soumis - Inverse optimal control problem in the non autonomous linear-quadratic case
and
soumis
2024
- Statistical Linearization for Robust Motion Planning
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Systems and Control Letters, vol. 189, pp. 105825, Elsevier, may, 2024
2023
- Deterministic optimal control on Riemannian manifolds under probability knowledge of the initial condition
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SIAM Journal on Mathematical Analysis, Society for Industrial and Applied Mathematics, 2023 - On the Accessibility and Controllability of Statistical Linearization for Stochastic Control: Algebraic Rank Conditions and their Genericity
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Mathematical Control and Related Fields, AIMS, 2023 - Robust Motion Planning of the Powered Descent of a Space Vehicle
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IFAC-PapersOnLine, vol. 56 (2), pp. 2001-2006, Elsevier, 2023
2022
- Lp-asymptotic stability of 1D damped wave equations with localized and linear damping
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ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, jan, 2022 - Structure of optimal control for planetary landing with control and state constraints
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ESAIM: Control, Optimisation and Calculus of Variations, vol. 28, EDP Sciences, 2022
2021
- On Weyl's type theorems and genericity of projective rigidity in sub-Riemannian Geometry
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Geometriae Dedicata, vol. 213 (1), pp. 295-314, Springer Verlag, 2021
2020
- A Geometrical Approach for the Optimal Control of Sequencing Batch Bio-Reactors
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Statistics, Optimization & Information Computing, 2020 - Efficient computation of optimal open-loop controls for stochastic systems
and
Automatica, vol. 115, 2020 - On the regularity of abnormal minimizers for rank 2 sub-Riemannian structures
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Journal de Mathématiques Pures et Appliquées, vol. 133, pp. 118-138, 2020 - Periodical body's deformations are optimal strategies for locomotion
and
SIAM Journal on Control and Optimization, vol. 38, Issue 8, pp. 1700-1714, 2020 - Stochastic optimal open-loop control as a theory of force and impedance planning via muscle co-contraction
and
PLOS Computational Biology, vol. 16(2): e1007414, 2020
2019
- Horizontal holonomy and foliated manifolds
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Annales de l'Institut Fourier, vol. 69 (3), pp. 1047-1086, Association des Annales de l'Institut Fourier, 2019 - On projective and affine equivalence of sub-Riemannian metrics
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Geometriae Dedicata, vol. 203(1), pp. 279--319, Springer Verlag, 2019
2018
- On measures in sub-Riemannian geometry
and
Séminaire de Théorie spectrale et géométrie (Grenoble), vol. 33 (2015-2016), pp. 17--46, 2018
2017
- Inverse Optimal Control Problem: the Sub-Riemannian Case
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IFAC-PapersOnLine, vol. 50, pp. 500--505, 2017
2016
- Why Don't We Move Slower? The Value of Time in the Neural Control of Action
and
The Journal of Neuroscience, vol. 36 (4), pp. 1056-1070, jan, 2016
2015
- Complexity of control-affine motion planning
and
SIAM Journal on Control and Optimization, vol. 53 (2), pp. 816--844, 2015 - Hausdorff volume in non equiregular sub-Riemannian manifolds
and
Nonlinear Analysis: Theory, Methods & Applications, pp. 345--377, 2015
2014
- Commande optimale en temps minimal d’un procédé biologique d’épuration de l’eau
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ARIMA, vol. 18, 2014
2013
- A Global Steering Method for Nonholonomic Systems
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Journal of Differential Equations, vol. 254, pp. 1903--1956, 2013 - A new class of $({\cal H}^k,1)$-rectifiable subsets of metric spaces
and
Com. on Pure and Applied Analysis, vol. 12, pp. 881--898, 2013 - On the inverse optimal control problems of the human locomotion: stability and robustness of the minimizers
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Journal of Mathematical Sciences, vol. 195, pp. 269--287, 2013
2012
- Optimal control models of the goal-oriented human locomotion
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SIAM J. Control and Optimization, vol. 50 (1), 2012
2010
- A biomechanical inactivation principle
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Proceedings of the Steklov Institute of Mathematics, vol. 268, pp. 93--116, 2010
2009
- A biomechanical theory of inactivation
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Computer Methods in Biomechanics and Biomedical Engineering, vol. 12, N. 1 supp 1, Taylor & Francis, 2009
2008
- Singular trajectories of control-affine systems
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SIAM J. Control Optim., vol. 47 (2), pp. 1078--1095, 2008 - The Inactivation Principle: Mathematical Solutions Minimizing the Absolute Work and Biological Implications for the Planning of Arm Movements
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PLoS Computational Biology, oct, 2008
2006
- Genericity results for singular curves
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Journal of Differentiel Geometry, vol. 73 (1), pp. 45--73, 2006
2004
- Nonhomogeneous nilpotent approximations for systems with singularities
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IEEE Transactions on Automatic Control, vol. 49(2), pp. 261-266, 2004
2003
- Entropy and Complexity of a Path in Sub-Riemannian Geometry
ESAIM: Cont. Opt. Calc. Var, vol. 9, pp. 485-506, 2003 - Generic properties of singular trajectories
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C. R. Acad. Sci. Paris, Ser. I, vol. 337 (1), pp. 49-52, 2003 - Measures of Transverse Paths in Sub-Riemannian Geometry
and
Journal d'Analyse Mathematique, vol. 91(1), pp. 231-246, dec, 2003
2001
- Complexity of Nonholonomic motion planning
International Journal of Control, vol. 74(8), pp. 776-782, 2001 - Uniform Estimation of Sub-Riemannian Balls
Journal on Dynamical and Control Systems, vol. 7 (4), pp. 473-500, oct, 2001
1998
- Multiplicity of Polynomials on Trajectories of Polynomials Vector Fields in C3
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Banach Center Publications, vol. 44(1), pp. 109-121, Singularities Symposium - Lojasiewicz 70, Institute of Mathematics Polish Academy of Sciences, 1998
1996
- The Car with N Trailers: Characterization of the Singular Configurations
ESAIM: Cont. Opt. Calc. Var, vol. 1, 1996
Livres
2017
2014
- Control of Nonholonomic Systems: from Sub-Riemannian Geometry to Motion Planning
Springer International Publishing, SpringerBriefs in Mathematics, 2014
2011
- Stabilité et Commande des Systèmes Dynamiques. Cours et exercices corrigés
Coll. Les Cours, Les Presses de l'ENSTA, 200 pages, nov 2011
Chapitres
2019
- Optimality and modularity in human movement: from optimal control to muscle synergies
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in Biomechanics of Anthropomorphic Systems, G. Venture, J-P. Laumond and B. Watier (Eds), vol. 124, pp. 105--133, Springer International Publishing, 2019
2017
- On the duration of human movement: from self-paced to slow/fast reaches up to Fitts's law
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In Geometric and Numerical Foundations of Movements, J-P. Laumond, N. Mansard, and J-B. Lasserre (Eds.), Springer International Publishing, 2017
2015
- La mécanique des Sphères de Lie: un futur pour la CAO?
et
Des mathématiques au monde socio-économique, vol. 28, Publications de la SMF, 2015
2014
- Hausdorff measures and dimensions in non equiregular sub-Riemannian manifolds
and
Geometric Control and sub-Riemannian geometry, vol. 5, Springer INdAM Series, 2014
2000
- Paths in Sub-Riemannian Geometry
Nonlinear Control in the Year 2000, Springer (A. Isidori, F. Lamnabhi-Lagarrigue and W. Respondek Eds.), 2000
1998
- Geometry of Nonholonomic Systems
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Robot Motion Planning and Control, vol. 229, Springer (J.-P. Laumond Ed.), 1998
Conférences internationales avec actes
2022
- A Mayer optimal control problem on Wasserstein spaces over Riemannian manifolds
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IFAC-PapersOnLine, vol. 55 (16), pp. 44-49, Elsevier, 2022 - Optimal planetary landing with pointing and glide-slope constraints
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2022 61th IEEE Conference on Decision and Control (CDC), apr, 2022
2019
- Injectivity of the inverse optimal control problem for control-affine systems
and
2019 IEEE Conference on Decision and Control (CDC), Nice, France, dec, 2019
2018
- Dual Particle Output Feedback Control based on Lyapunov drifts for nonlinear systems
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pp. 250-255, 2018 IEEE Conference on Decision and Control (CDC) (Miami Beach), dec, 2018 - Inverse Optimal Control Problem: The Linear-Quadratic Case
and
2018 IEEE Conference on Decision and Control (CDC), 2018 IEEE Conference on Decision and Control (CDC) (Miami Beach), dec, 2018
2017
- Nonlinear Fisher Particle Output Feedback Control and its application to Terrain Aided Navigation
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pp. 1566--1571, 2017 IEEE 56th Annual Conference on Decision and Control (CDC), Melbourne, 2017
2013
- Commande optimale en temps minimal d'un procédé biologique d'épuration de l'eau
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pp. 225-226, Proceedings of the International Joint Conference CB-WR-MED Conference/ 2nd AOP' Tunisia Conference for Sustainable Water Management. Tunis: April, 24―27, (Tunis), 2013 - Geometric modeling of the movement based on an inverse optimal control approach
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52th IEEE Conference on Decision and Control, Firenze, Italy, 2013
2012
- Commande optimale en temps minimal d’un procédé biologique d’épuration de l’eau
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CARI'12, Colloque Africain sur la Recherche en Informatique et en Mathématiques Appliquées (CARI’2012) (Alger), 2012
2011
- Biologically Inspired Sensory Motor Control of a 2-Link Robotic Arm Actuated by McKibben Muscles
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2011 IEEE International Conference on Robotics and Automation, 2011
2010
- An explicit desingularization procedure for general nonholonomic systems
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49th IEEE Conference on Decision and Control, Atlanta, 2010 - Analysis of optimal control models for the human locomotion
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49th IEEE Conference on Decision and Control, Atlanta, 2010
2009
- A global steering method for general dynamical nonholonomic systems
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48th IEEE Conference on Decision and Control, Shangai, 2009 - Asymptotic analysis of an optimal control problem connected to the human locomotion
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48th IEEE Conference on Decision and Control, Shangai, 2009
2005
- A globally convergent steering algorithm for regular nonholonomic systems
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44th IEEE CDC-ECC'05, Séville, Spain, 2005 - Singular trajectories of driftless and control-affine systems
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44th IEEE CDC-ECC'05, Séville, Spain, 2005
2002
- Measures of Sub-Riemannian Paths
and
1st Junior European Conference on Control Theory and Stabilization, Dijon, 2002
1997
- Elementary Approximation of Exponentials of Lie Polynomials
and
vol. 1255, 12th AAECC Symp., Springer (T. Mora and H. Mattson Eds.), 1997
1995
- The Singular Locus for the n Trailers Car Control System
34th IEEE CDC, New Orleans, LA, 1995
Conférences sans actes
2013
- A geometrical approach for the resolution of an optimal control problem. 2013
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International Conference on Advances in Applied Mathematics ICAAM-2013, Dec 2013, Hammamet, Tunisia, 2013 - Goal-oriented locomotion: the inverse optimal approach
SADCO Internal Meeting, 21-25 January 2013, Funchal, Portugal, 2013
2012
- A new class of (H^k,1)-rectifiable subsets of metric spaces.
INDAM meeting on Geometric Control and sub-Riemannian Geometry Cortona, Italy, May 21 - 25, 2012 - Contrôle des systèmes non-holonomes et géométrie sous-riemannienne (mini-cours)
Ecole de recherche CIMPA "Géométrie sous-riemannienne", Beyrouth, Liban, 30 janvier - 9 février, 2012 - Minimization principles in human motions: the inverse optimal control approach
PICOF'12, Inverse Problems, Control and Shape Optimization, Ecole Polytechnique, Palaiseau, April 2 - 4, 2012
2011
- Minimization principles in human motions and inverse optimal control
Contrôle, Imagerie et Probabilités en Méditerranée, Université de Nice Sophia-Antipolis, 24 -- 28 octobre, 2011 - Nonholonomic control systems: nilpotent approximations, desingularization and steering by sinusoidal controls
Vector Distributions and sub-Riemannian Systems, Banach Center, Warsaw, March 30 -- April 1, 2011 - Principes de minimisation dans les mouvements humains: l'approche par le contrôle optimal inverse
Journée du GT8 Robotique et Neurosciences du GDR Robotique, Paris, 23 Juin, 2011
2010
- Analysis of an optimal control problem modeling the human locomotion
Premières journées scientifiques du Laboratoire Euro Maghrébin de Mathématiques et de leurs Interactions (LEM2I), Tipaza, Algérie, 13 22 juin, 2010 - On Hausdorff Measures of Curves in Sub-Riemannian Geometry
New Trends in Sub-Riemannian Geometry, University of Nice, March 29 -- April 2, 2010 - On Hausdorff Measures of Curves in Sub-Riemannian Geometry
Géométrie sous-riemannienne et singularités, Chambéry, 14 et 15 octobre, 2010 - Optimal control models of the goal-oriented human locomotion
Workshop on Nonlinear Control and Singularities, Porquerolles, France, October 24th-28th, 2010 - Tangent cone and Hausdoff measure of curves
Franco-Brazilian Workshop on Sub-Riemannian Geometry, Belem, August 23-27, 2010
2009
- Asymptotic analysis of an optimal control problem connected to the human locomotion
48th IEEE Conference on Decision and Control, Shanghai, China, December 16-18,, 2009 - Asymptotic analysis of an optimal control problem modeling the human locomotion
14th Belgian-French-German Conference on Optimization, Leuven, September 14-18, 2009
2008
- On Rectifiability and Hausdorff Measures of Curves in Sub-Riemannian Geometry
Differential Equations and Topology, Moscow, June 17--22, 2008
2007
- Singular trajectories of control-affine systems
13th Czech-French-German Conference on Optimization, Heidelberg, 2007
2006
- Generic results for horizontal and singular curves of rank-varying distributions
Workshop on "Geometry of vector distributions, differential equations, and variational problems", SISSA, Trieste, 2006
2005
- Genericity results for singular tra jectories
22nd IFIP TC 7 Conference on System Modeling and Optimization, Turin, 2005
2004
- Singular curves in sub-Riemannian geometry : generic properties and optimality status
Colloquia on Control Theory and Partial Differential Equations, CNR-IAC et Universités "La Sapienza" et "Tor Vergata", Rome, 2004
2003
- Genericity results for singular curves
Workshop on geometry in nonlinear control, Banach Center, Pologne, 2003 - Iterative steering methods for generic driftless control systems
Meeting on Control Theory and Stabilization, Université de Turin, 2003
2002
- Gromov's metric tangent cone of a SR manifold
4th Conference on Dynamical System and Differentiable Equations, University of North Carolina, 2002
Séminaires
2013
- Principes de minimisation dans les mouvements humains et contrôle optimal inverse
Séminaire Mécanique et géométrie, Institut de Mathématiques de Jussieu, mar 2013 - Volumes de Hausdorff en géométrie sous-riemannienne
Colloquium de l'Institut de Mathématiques de Bourgogne, jun 2013
2012
- Principes de minimisation dans les mouvements humains: l'approche par le contrôle optimal inverse
Séminaire du CAS, Mines Paris, nov 2012 - Principes de minimisation dans les mouvements humains: l'approche par le contrôle optimal inverse
Séminaire MOD, Université de Limoges, jun, 2012
2010
- Un principe dinactivation pour la planification motrice des mouvements du bras
Séminaire CMAP -- 13 avril, 2010
2009
- Un principe dinactivation pour la planification motrice des mouvements du bras
Séminaire ISIR, Jussieu, 5 février, 2009
2008
- Courbes singulières dune distribution
Séminaire Université de Savoie, Chambéry, 28 mars, 2008 - Sur la synthèse optimale dun modèle de locomotion humaine
Séminaire du LAAS, Toulouse, 11 janvier, 2008
2006
- Algorithmes pour la planification de mouvements en robotique non holonome
Séminaire CEP Arcueil-ENSTA, fév 2006
Thèse d'Habilitation
2007
- Géométrie sous-riemannienne et contrôle non-linéaire
Habilitation à Diriger les Recherches de l'Université Pierre et Marie Curie (spécialité: mathématiques), mar 2007 [ ]
Thèse
1998
- Complexités pour les systèmes non-holonomes
Thèse de doctorat de l'Université Pierre et Marie Curie (spécialité : mathématiques), jan 1998
Rapports de recherche
2013
- Control of Nonholonomic Systems and Sub-Riemannian Geometry
eprint arXiv:1209.4387, Ecole de recherche CIMPA "Géométrie sous-riemannienne", Beyrouth, Liban, 30 janvier - 9 février 2012, 2013
2008
- An Approximate Algorithm for Nonholonomic Motion Planning
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Preprint CMAP N. 651, dec, 2008 [ ]
2006
- On Hausdorff Measures of Curves in Sub-Riemannian Geometry
Preprint du CMAP, École Polytechnique, nov, 2006
Cours
2021
- Géométrie Différentielle et Application au Contrôle Géométrique
Cours AOT13, mai 2021