UMA Home page for Frédéric Jean
Teaching/Research
Dir. UMA
Professor
Dir. UMA
Professor
Research Habilitation 2007
Ph.D. 1998
EMAIL_TEMPLATE
Research activities
Since my PhD in Mathematics at the University Pierre et Marie Curie (Paris 6) in 1998, I am teacher and researcher in the group Optimization and Control of the Department of Applied Mathematics (UMA) of ENSTA. I am at the moment Director of UMA.
My research activities fall within the context of the non-linear control theory, and more specifically the one of Geometric Control. My research focuses firstly on theoretical aspects: sub-Riemannian geometry, non-holonomic systems, geometric approach to optimal control; and secondly on modeling neurophysiology through controlled system, mainly by identification of principles of minimization (inverse optimal control problems).
I was part of the organizing committee of the Quarter IHP "Geometric analysis and dynamics on sub-Riemannian manifolds'', Paris, September 1 - December 13, 2014.
PhD students:
- Ruixing Long (co-supervision with Yacine Chitour), defended in 2010;
- Dario Prandi (co-supervision with Ugo Boscain, Mario Sigalotti), defended in 2013;
- Cristopher Hermosilla (co-supervision with Hasnaa Zidani), defended in 2015;
- Boutheina Hafassa (co-supervision with Yacine Chitour, Mario Sigalotti), defended in 2016;
- Walid Bouhafs (co-supervision with Nahla Abdellatif), defended in 2016;
- Sofya Maslovskaya (co-supervision with Igor Zelenko), defended in 2018;
- Emilien Flayac (co-supervision with Karim Dahia et Bruno Hérissé), defended in 2019
- Meryem Kafnemer (co-supervision with Yacine Chitour), defended in 2022;
- Othmane Jerhaoui (co-supervision with Hasnaa Zidani), defended in 2022;
- Clara Leparoux (co-supervision with Bruno Hérissé), since 2020;
Teaching activities
Responsible for the M1 Applied Mathematics - Site Palaiseau, University Paris-Saclay.
Teaching at M2 level:
- the course Geometric Control, with Boscain U. and Y. Chitour, M2 Optimization of the University of Paris-Saclay;
- the course Motion planning, with H. Zidani, M2 ATSI of the University of Paris-Saclay; this course is also part of the 3rd year of ENSTA, under the symbol OROC-SC-PL.
Teaching in Research schools:
- Sub-Riemannian geometry (~15h), Trimester Dynamical and Control Systems, Trieste (octobre 2003);
- Control of Nonholonomic Systems and Sub-Riemannian Geometry (~6h), CIMPA research school Sub-Riemannian Geometry, Beyrouth (2012);
- Planification des mouvements pour les systèmes non-holonomes (~7h), CIMPA research school Contrôle géométrique, stochastique et des équations aux dérivées partielles, Tlemcen (2014);
- Geodesics in sub-Riemannian manifolds (~24h), with Andrei Agrachev, IHP Trimestre
Geometry, Analysis and Dynamics on
Sub-Riemannian Manifolds, Paris (2014);
→ VIDEO recording available here.
Other activities
List of publications (HAL)
Publications
Papers in peer-reviewed journals
Submitted
- A unifying vision of Particle Filtering and Explicit Dual Control
, , and
submitted
- Deterministic optimal control on Riemannian manifolds under probability knowledge of the initial condition
, and
submitted - Statistical Linearization for Robust Motion Planning
, , and
submitted 
To appear
- On the Accessibility and Controllability of Statistical Linearization for Stochastic Control: Algebraic Rank Conditions and their Genericity
, , and
Mathematical Control and Related Fields (MCRF), to appear
2022
- Lp-asymptotic stability of 1D damped wave equations with localized and linear damping
, , and
ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, jan, 2022 - Structure of optimal control for planetary landing with control and state constraints
, and
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
, and
Geometriae Dedicata, vol. 213 (1), pp. 295-314, Springer Verlag, 2021
2020
- A Geometrical Approach for the Optimal Control of Sequencing Batch Bio-Reactors
, , and
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
, , , and
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
, , and
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
, and
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
, and
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
, , et
ARIMA, vol. 18, 2014
2013
- A Global Steering Method for Nonholonomic Systems
, and
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
, and
Journal of Mathematical Sciences, vol. 195, pp. 269--287, 2013 
2012
- Optimal control models of the goal-oriented human locomotion
, and
SIAM J. Control and Optimization, vol. 50 (1), 2012
2010
- A biomechanical inactivation principle
, and
Proceedings of the Steklov Institute of Mathematics, vol. 268, pp. 93--116, 2010
2008
- Singular trajectories of control-affine systems
, and
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
, , , , and
PLoS Computational Biology, oct, 2008
2006
- Genericity results for singular curves
, and
Journal of Differentiel Geometry, vol. 73 (1), pp. 45--73, 2006
2004
- Nonhomogeneous nilpotent approximations for systems with singularities
, , and
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
, and
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
, and
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
Books
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
Chapters
2019
- Optimality and modularity in human movement: from optimal control to muscle synergies
, , and
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
and
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
, and
Robot Motion Planning and Control, vol. 229, Springer (J.-P. Laumond Ed.), 1998
International conferences with proceedings
2022
- A Mayer optimal control problem on Wasserstein spaces over Riemannian manifolds
, and
IFAC-PapersOnLine, vol. 55 (16), pp. 44-49, Elsevier, 2022 - Optimal planetary landing with pointing and glide-slope constraints
, and
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
, , and
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
, , and
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
, , et
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
, and
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
, , et
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
, , , , and
2011 IEEE International Conference on Robotics and Automation, 2011
2010
- An explicit desingularization procedure for general nonholonomic systems
, and
49th IEEE Conference on Decision and Control, Atlanta, 2010 - Analysis of optimal control models for the human locomotion
, , and
49th IEEE Conference on Decision and Control, Atlanta, 2010
2009
- A biomechanical theory of inactivation
, and
Computer Methods in Biomechanics and Biomedical Engineering, vol. 12, N. 1 supp 1, Taylor & Francis, 2009 - A global steering method for general dynamical nonholonomic systems
, and
48th IEEE Conference on Decision and Control, Shangai, 2009 - Asymptotic analysis of an optimal control problem connected to the human locomotion
, , and
48th IEEE Conference on Decision and Control, Shangai, 2009
2005
- A globally convergent steering algorithm for regular nonholonomic systems
, and
44th IEEE CDC-ECC'05, Séville, Spain, 2005 - Singular trajectories of driftless and control-affine systems
, and
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
Conferences without proceedings
2013
- A geometrical approach for the resolution of an optimal control problem. 2013
, , and
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
Seminars
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
Habilitation these
2007
- Géométrie sous-riemannienne et contrôle non-linéaire
Habilitation à Diriger les Recherches de l'Université Pierre et Marie Curie (spécialité: mathématiques), mar 2007 [ ]
Doctoral these
1998
- Complexités pour les systèmes non-holonomes
Thèse de doctorat de l'Université Pierre et Marie Curie (spécialité : mathématiques), jan 1998
Research reports
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
, , and
Preprint CMAP N. 651, dec, 2008 [ ]
2006
- On Hausdorff Measures of Curves in Sub-Riemannian Geometry
Preprint du CMAP, École Polytechnique, nov, 2006
Preprint
Submitted
- Statistical Linearization for Robust Motion Planning
, , and
submitted
Lecture note
2021
- Géométrie Différentielle et Application au Contrôle Géométrique
Cours AOT13, mai 2021