Page UMA de Hasnaa Zidani
Zidani
Hasnaa
Équipe OC
Activités de recherche
Ma recherche s'articule autour de deux thèmes principaux: d'une part l'optimisation des systèmes dynamiques, et d'autre part l'analyse mathématique et numérique des équations Hamilton-Jacobi-Bellman (HJB) du premier et second ordre. Plus précisément, je travaille actuellement sur les thèmes suivants:
Responsabilité scientifique et coordination des programmes de recherche:
Logiciel:
- Approche HJB pour la planification de trajectoires: commande des systèmes nolinéaires avec contraintes sur l'état et sans hypothèse de
contrôlabilité, reconstruction du feedback optimal, commande des trajectoires discontinues. Ce thème est supporté par un financement de la Direction Générale de l'Armement - DGA- 2007-2009 et 2010-2013.
Application: optimisation de trajectoire pour des lanceurs de type Ariane (collaboration avec O. Bokanowski, P. Martinon). Ce thème est soutenu par le Centre Nationale d'Etudes Spatiales - Cnes- de 2006--2010.
- Commande des systèmes hybrides par approche HJB. Application à la gestion d'énergie d'un véhicule hybride (collaboration avec Renault-Technocentre 2008-2012.
Thèse cifre de G. Granato, soutenue en décembre 2012)
- Réalisation d'une bibliothèque numérique en calcul parallèle pour la résolution des équations HJB du premier et second ordre (collaboration avec O. Bokanowski et J. Zhao, en partenariat avec HPC Project, 2010-2012).
- Théorie de l'estimation d'erreur pour l'approximation des équations HJB: systèmes d'équations HJB du second ordre, estimation à posteriori de schémas monotones pour des inéquations variationnelles, analyse de l'erreur pour l'approximation de systèmes d'inéquations quasi-variationnelles.
Responsabilité scientifique et coordination des programmes de recherche:
- FP7 European project SADCO - Sensitivity Analysis for Deterministic Controller Design, (Marie Curie ITN-264735), 2011 -- 2014
- "Trajectory Optimisation for the space launcher Ariane V" (with O. Bokanowski, A. Désilles), supported by CNES, 2006 - 2010 and 2012-2013
- DGA Grant 2007-09 "HJB approach for motion planning"; 2009-12 "Trajectory optimization for complex dynamical systems"; 2012-15 "Optimal control problems with uncertainties and probabilistic state constraints"
- "Energy management for Hybrid vehicles", supported by Renault-Technocentre, 2009 - 2012
Logiciel:
- ROC-HJ "Reachability analysis and Optimal Control problems. Hamilton-Jacobi equations". Ce logiciel en C++ résoud une large classe d'équations HJ provenants de problèmes de commande optimale (temps d'arrêt, contrôle en horizon infine, problèmes avec contraintes d'état, temps minimal, analyse d'atteignabilité et évitement d'obstacles, jeux différentiels). Le logiciel inclut la reconstruction de trajectoires optimales.
Voir http://uma.ensta-paris.fr/files/ROC-HJ
Activités d'enseignement
A l'Ensta, je suis responsable du module "B7: Commande des Systèmes". Je suis aussi enseignante principale des cours:
- AO101:"Optimisation quadratique". Cours de Tronc Commun de 1ère Année à l'ENSTA
- D11-4: "Approximation numérique pour la propagation des fronts d'ondes". Cours de 3e année à l'Ensta et Master Modélisation et Simulation.
Je participe aussi à ce cours à l'ECP avec Ch. Chalons.
- "Commande optimale des systèmes nonlinéaires". Cours de 3e année à l'Ensta (aussi Cours de Master 2 à l'Université d'Orsay (2006-2010)).
Autres activités
- Co-responsable de l'équipe projet COMMANDS (Inria Saclay, ENSTA Paris, Ecole Polytechnique) de 2007 à 2014.
- Membre titulaire du CNU (26e section) de 2011 à 2017.
- Membre du SMAI-MODE council, depuis 2016.
- Membre élu du conseil scientifique de la " FMJH- Fondation Mathématique Jacques Hadamard", depuis 2016.
- Membre titulaire du CNU (26e section) de 2011 à 2017.
- Membre du SMAI-MODE council, depuis 2016.
- Membre élu du conseil scientifique de la " FMJH- Fondation Mathématique Jacques Hadamard", depuis 2016.
Publications
Articles (revues avec comité de lecture)
- Bi-objective finite horizon optimal control problems with Bolza and maximum running cost
and
soumis
- Deterministic optimal control on Riemannian manifolds under probability knowledge of the initial condition
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soumis
- Global Optimization Approach for the Ascent Problem of Multi-stage Launchers
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Modeling, Simulation and Optimization of Complex Processes HPSC 2018. Springer, Cham., pp. 1--42, Bock H.G., Jäger W., Kostina E., Phu H.X. (eds), 2021
- Demand response versus storage flexibility in energy: multi-objective programming considerations
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Journal Optimization, 2020 - Stability and Reachability analysis for a controlled heterogeneous population of cells
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Optimal Control, Applications & Methods, vol. 41(5), pp. 1678--1704, 2020
- Junction conditions for finite horizon optimal control problems on multi-domains with continuous and discontinuous solutions
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ESAIM: Control, Optimisation, and Calculus of Variations, vol. 25(79), pp. 38, 2019 - Pareto Front Characterization for Multiobjective Optimal Control Problems Using Hamilton--Jacobi Approach
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SIAM J. on Control and Optimization, vol. 57 (6), pp. 3884-3910, SIAM, 2019
- Error estimates for numerical approximation of Hamilton-Jacobi equations related to hybrid control systems
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Applied Mathematics & Optimization, 2018 - Infinite Horizon Stochastic Optimal Control Problems with Running Maximum Cost
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SIAM J. Control Optim., vol. 56(5), pp. 3296--3319, 2018 - Optimal control of normalized SIMR models with vaccination and treatment
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Discrete and Continuous Dynamical Systems - Series B, vol. 23 (1), pp. 79 - 99, 2018 - Solving chance constrained optimal control problems in aerospace via Kernel Density Estimation
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Optimal Control, Applications and Methods, vol. 39(5), pp. 1818-1832, 2018 - Value function and optimal trajectories for a maximum running cost control problem with state constraints. Application to an abort landing problem.
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ESAIM: Mathematical Modelling and Numerical Analysis (ESAIM: M2AN), vol. 52(1), pp. 305--335, 2018
- Discontinuous solutions of Hamilton-Jacobi equations on networks *
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Journal of Differential Equations, vol. 263 (12), pp. 8418-8466, Elsevier, 2017 
- Hamilton-Jacobi-Bellman equations for optimal control processes with convex state constraints
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Systems and Control Letters, vol. 109, pp. 30–36, Elsevier, 2017 - The Mayer and Minimum Time Problems with Stratified State Constraints
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Set-Valued and Variational Analysis, Springer, 2017
- State-constrained stochastic optimal control problems via reachability approach
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SIAM J. on Control and Optimization, vol. 54 (5), pp. 2568–2593, 2016
- Dynamic programming and error estimates for stochastic control problems with maximum cost
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Applied Mathematics and Optimization (AMO, Springer), vol. 71(1), pp. 125--163, 2015 - Error Estimates for Second Order Hamilton-Jacobi-Bellman Equations. Approximation of Probabilistic Reachable Sets
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DCDS- Serie A, vol. 35(9), pp. 3933 - 3964, 2015 - Infinite horizon problems on stratifiable state-constraints sets
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Journal of Differential Equations, vol. 258(4), pp. 1420--1460, 2015 - Monotone numerical schemes and feedback construction for hybrid control systems
and
J. of Optimization Theory and Applications, vol. 165(2), pp. 507-531, 2015 - Optimal feedback control of undamped wave equations by solving a HJB equation
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ESAIM: Control, Optimisation, and Calculus of Variations, vol. 21(2), pp. 442 - 464, 2015 - Value iteration convergence of ℇ-monotone schemes for stationary Hamilton-Jacobi equations
, , , , and
Discrete and Continuous Dynamical Systems - Serie A, vol. 35(9), pp. 4041 - 4070, 2015 - Zubov's equation for state-constrained perturbed nonlinear systems
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Mathematical Control and Related Fields, vol. 5(1), pp. 55 - 71, 2015
- Level-set approach for Reachability Analysis of Hybrid Systems under Lag Constraints
and
SIAM J. Control and Optim., vol. 52, pp. 606-628, 2014 - Transmission conditions on interfaces for Hamilton-Jacobi-Bellman equations
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Journal of Differential Equations, vol. 257(11), pp. 3978--4014, 2014
- A Hamilton-Jacobi approach to junction problems and application to traffic flows
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ESAIM: Control, Optimisation, and Calculus of Variations., vol. 19(01), pp. 129--166, 2013 - A general Hamilton-Jacobi framework for nonlinear state-constrained control problems
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ESAIM: Control, Optimisation, and Calculus of Variations., vol. 19(2), pp. 337--357, 2013 - State-Constrained Optimal Control Problems of Impulsive Differential Equations
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Applied Mathematics & Optimization, vol. 68, pp. 1--19, 2013
- Approximation schemes for monotone systems of nonlinear second order partial differential equations: convergence result and error estimate
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Differential Equations and Applications, vol. 4, pp. 297--317, 2012
- Characterisation of the value function of final state constrained control problems with BV trajectories
and
Communication in Pure and Applied Analysis., vol. 10(6), pp. 1567-1587, 2011 [
] - Deterministic state constrained optimal control problems without controllability assumptions
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ESAIM: Control, Optimisation and Calculus of Variations., vol. 17(04), pp. 975--994, 2011 [ ]
- An efficient data structure and accurate scheme to solve front propagation problems
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Journal of Scientific Computing., vol. 42(2), pp. 251--273, 2010 [ ] - Convergence of a non-monotone scheme for Hamilton-Jacobi-Bellman equations with discontinuous initial data
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Numerische Mathematik., vol. 115(1), pp. 1--44, 2010 [ ] - L¹-error estimates for numerical approximations of Hamilton-Jacobi-Bellman equations in dimension 1
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Mathematics of Computation., vol. 79(271), pp. 1395--1426, 2010 [ ] - Reachability and minimal times for state constrained nonlinear problems without any controllability assumption
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SIAM J. Control and Optimization., vol. 48(7), pp. 4292-4316, 2010 [ ]
- Minumum time control problems for non autonomous differential equations
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Systems and Control Letters, vol. 58(10-11), pp. 742-746, 2009 - Numerical approximation for a superreplication problem under gamma constraints
, , and
SIAM. J. of Num. Analysis., vol. 47(3), pp. 2289-2320, 2009 [ ] - Some convergence results for Howard's algorithm
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SIAM J. of Num. Analysis., vol. 47(4), pp. 3001--3026, 2009 [ ]
- Anti-dissipative schemes for advection and application to Hamilton-Jacobi-Bellman equations
and
J. Sci. Computing, vol. 30(1), pp. 1--33, 2007 [ ] - Error estimates for a stochastic impulse control problem
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Applied. Math. and Optimisation, vol. 55-3, pp. 327--357, 2007 [ ]
- A method for optimal control problems : an adaptative antidissipative method for optimal control problems
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Revue Africaine de la Recherche en Informatique et Mathématiques Appliquées, vol. 5, pp. 256-271, 2006 - An anti-diffusive scheme for viability problems
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Applied Numerical Methematics, vol. 56(9), pp. 1147--1162, 2006 [ ] - Error estimates for stochastic differential game: the adverse stopping case
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IMA Journal of Numerical Analysis, vol. 28, pp. 188-212, 2006 [ ]
- Consistency of a simple multidimensional scheme for Hamilton–Jacobi–Bellman equations
and
Comptes Rendus Mathematique, vol. 340(7), pp. 499–502, apr, 2005 [ ]
- A fast algorithm for the two dimensional HJB equation of stochastic control
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ESAIM: Mathematical Modelling and Numerical Analysis, vol. 38(4), pp. 723-735, 2004 [ ] - Parametric optimization of hybrid car engines
, , , and
Optimization and Engineering, vol. 5(4), pp. 395-415, dec, 2004
- Consistency of Generalized Finite Difference Schemes for the Stochastic HJB Equation
and
SIAM Journal on Numerical Analysis, vol. 41(3), pp. 1008-1021, 2003 [ ] - Discrete approximation for a class of the Hamilton-Jacobi equation for an optimal control problem of a differential-algebraic system
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Control and Cybernetics, vol. 32-1, pp. 33-55, 2003
- A fully Discrete Approximation for a Control Problem of Parabolic Variational Inequalities
and
SIAM Journal on Numerical Analysis, vol. 39(6), pp. 2014-2033, 2002 [ ]
- Pontryagin Principle for Local Solutions of Control Problems with mixed State Control Constraints
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SIAM J. Control and Optimization, vol. 39-4, pp. 1182--1203, 2000 [ ] - Time optimal problems with boundary controls
and
Differential and Integral Equations, vol. 13(7-9), pp. 1039--1072, 2000 [ ]
- Hamiltonian Pontryagin's Principles for Control Problems Governed by Semilinear Parabolic Equations
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Applied Mathematics and Optimization, vol. 39 (2), pp. 143-177, 1999 [ ] - On the minimization of the energy of a free-electron gas with constrained density function
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Nonlinear Analysis, Theory, Methods and Applications, vol. 35 (8), pp. 1073-1090, 1999 - Optimal control problems with partially polyhedric constraints
and
SIAM J. on Control and Optimization, vol. 37(6), pp. 1726--1741, 1999 [ ] - Pontryagin maximum principle for optimal control of variational inequalities
and
SIAM J. on Control and Optimization, vol. 37 (4), pp. 1273-1290, 1999 [ ] - Pontryagin's principle for time-optimal problems
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J. Optimization Theory and Applications, vol. 101(2), pp. 375--402, 1999
- Pontryagin's principle for state-constrained control problems governed by parabolic equations with unbounded controls
and
SIAM J. on Control and Optimization, vol. 36(6), pp. 1853--1879, 1998 [ ]
Chapitres
- Hamilton-Jacobi-Bellman Equations on Multi-Domains
and
Control and Optimization with PDE Constraints, International Series of Numerical Mathematics, vol. 164, pp. 93-116, Birkhäuser Basel, 2013
- Characterization of consistency of some numerical schemes for the stochastic HJB equation
and
Contrôle optimal et EDP - Innovations et Applications'', Ed. J.L. Menaldi et al, IOS Presse, 2000
- Optimal Control Problem Governed by Semilinear Elliptic Equations with Integral Control Constraints and Pointwise State Constraints
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Inter. Series. of Num. Math., W. Desch and F. Kappel Eds., Birkhaüser-Verlag, 1998
- Optimal Control Problem Governed by a Semilinear Parabolic Equation
and
System Modelling and Optimization, J. Dolezal and J. Fiedler Eds., Chapman and Hall, p. 211-217, 1996, pp. 211--217, J. Dolezal and J. Fiedler Eds., Chapman and Hall, 1996
Direction d'ouvrage
- Special issue on New trends in optimal control
, , , and
Discrete Contin. Dyn. Syst., vol. 35(9), AIMS, 2015
Conférences internationales avec actes
- 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
- Optimization of the launcher ascent trajectory leading to the global optimum without any initialization: the breakthrough of the HJB approach
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EUCASS Proceedings "Progress in Flight Dynamics, Guidance, Navigation, and Control",, vol. 10, pp. 159-176, Selected paper at the "6th European Conference for Aeronautics and Space Sciences - EUCASS", June 2015, Kraków, Poland., 2018
- A maximum principle for a special optimal multiprocess problem with state constraints
and
pp. 1566-1571, IEEE, Proceeding of the "11th Asian Control Conference (ASCC)", 2017 - New improvements in the optimization of the launcher ascent trajectory through the HJB approach
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Proceedings of "7TH EUROPEAN CONFERENCE FOR AERONAUTICS AND SPACE SCIENCES (EUCASS)", 2017, 15p., 2017 - Payload optimization for multi-stage launchers using HJB approach and application to a SSO mission
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vol. 50(1), pp. 2904-2910, The 20th IFAC World Congress (Toulouse), 2017
- A Hamilton-Jacobi-Bellman approach for the optimal control of an abort landing problem
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IEEE 55th Conference on Decision and Control (CDC), 2016, dec, 2016 - HJB approach for a multi-boost launcher trajectory optimization problem
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IFAC Proceedings, vol. 49-17, pp. 456-461, 20th IFAC Symposium on Automatic Control in Aerospace - ACA 2016, Aug 2016, Sherbrooke, Quebec, Canada., 2016
- Collision analysis for a UAV
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AIAA Guidance, Navigation and Control Conference, Minneapolis (USA), 13-16 August. Doi: 10.2514/6.2012-4526, vol. Chapt. 4526, pp. 23 pages, 2012 - Hamilton-Jacobi-Bellman approach for the climbing problem for multi-stage launchers
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pp. 8 pages, 20th International Symposium on Mathematical Theory of Networks and Systems (MTNS'2012), 2012
- A Stochastic Dynamic Principle for Hybrid Systems with Execution Delay and Decision Lags
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50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC) Orlando, FL, USA, December 12-15, 2011, pp. 6788-6793, 2011 - HJB approach for motion planning and reachabilty analysis
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Proceeding of the 5th International ICST Conference on Performance Evaluation Methodologies and Tools (ValueTools'2011), pp. 28--36, 2011 - Minimal time problems with moving targets and obstacles
and
Proceedings of the 18th IFAC World Congress. Doi: 10.3182/20110828-6-IT-1002.02261, vol. 18, pp. 2589-2593, 2011 - Optimal control problems of BV trajectories with pointwise state constraints
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Proceedings of the 18th IFAC World Congress, Milan. Doi: 10.3182/20110828-6-IT-1002.01694, vol. 18, pp. 2583-2588, 2011
Conférences sans actes
- Hamilton-Jacobi approach for multi-objective problems
International Workshop on "Optimal Control of Dynamical Systems" (Invited speaker), Mariatrost, Graz (Austria), May 15-19, 2017
- Value function and optimal trajectories for a control problem with supremum cost function and state constraints
Workshop "Numerical methods for Hamilton-Jacobi equations in optimal control and related fields" (Invited speaker), RICAM Institute, Linz (Austria), November 21-25, 2016
- NETCO - "New Trends on Optimal Control" - June 23-27, 2014.
H. Zidani (co-Organizer: Head Of The Organizing Committee & Member Of The Scientific Committee). This event is organised by the European ITN SADCO Project, with the participation of the French HJ-Net ANR project, 2014 - Optimal control problems on generalized networks (Invited speaker)
Workshop on "Geometric control and related fields", Special Semester on New Trends in Calculus of Variations, RICAM Institute, Linz (Austria), November 17-21, 2014 - Recent Advances in the Numerical Analysis of Optimal Hybrid Control Problems
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MTNS 2014 (Groningen), jul, 2014
- Collision avoidance for UAVs
Portuguese Meeting on Optimal Control, EPCO'2013 (invited talk), FEUP, Porto, February 7-8, 2013
- Organisation d'une session "Optimal control in constrained domains"
and
12th Viennese Workshop on Optimal Control, Dynamic Games and Nonlinear Dynamics, Wien (Austria), May 30th - June 2nd, 2012, 2012 - Organisation de 4 sessions "Optimisation-based controller design"
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20th International Symposium on Mathematical Theory of Networks and Systems, Melbourne, 9-13 July, 2012 - Organisation de la session "Policy iteration algorithms and some applications"
21th International Symposium on Mathematical Programming (ISMP'2012), 2012 - Organisation de la session "Differential games and engineering applications"
and
12th Viennese Workshop on Optimal Control, Dynamic Games and Nonlinear Dynamics, Wien, May 30th - June 2nd, 2012, 2012
- Hamilton-Jacobi approach in singular domains
International Workshop on "Control and Optimization of PDEs", Mariatrost, October 10-14, 2011 (invited speaker), 2011
- State-constrained control problems lacking controllability assumptions
9th Brazilian Conference on Dynamics, Control and Their Applications - Dincon'2010 (keynote speaker), 2010
- Minisymposium "Sensitivity Analysis of deterministic control systems : theory, numerical methods and applications"
organisé dans le cadre de la conférence "14 th Belgian-French-German Conference on Optimization". Leuven, September 14-18, 2009
- Aerospatial dynamics and Optimal Control
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ENSTA, 23 May, 2008 - Approximation numérique d'un probléme de sur-couverture
Congrès SM2A, Rabat, 6--8 February, 2008 - Ecole CEA-EDF-INRIA "Numerical methods for Hamilton-Jacobi equations and hyperbolic conservation laws"
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INRIA Rocquencourt, 15--19 September 2008, 2008 - Some theoretical and numerical results for Howard's algorithm.
Rencontres MATH-Amsud, 4-6 Novembre, Lima, 2008
- A fast anti-dissipative method for the minimal time problem. Application to atmospheric re-entry
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CODE-2007: Conférence de la SMAI sur l'Optimisation et la Décision. Paris, avr 2007 - A super-linear convergence result for Howard algorithm
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Second European Conference on Computational Optimization, Montpellier (France), apr, 2007 - An efficient implementation of arrow Band methods for Hamilton-Jacobi-Bellman equations
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Introduction to numerical methods for moving boundaries, nov, 2007 - Approximation numérique pour un problème de sur-couverture
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Conférence de la SMAI sur l'Optimisation et la Décision, Paris (France), avr 2007
- A fast anti-dissipative method for the atmospheric re-entry problem
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New trends in viscosity solutions and non linear PDE's. Lisboa, jul, 2006 - Analyse numérique pour un problème de sur-couverture en finance
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Journée "Théorie du contrôle", Université de Orsay, France, Décembre 2006., 2006 - Error estimate for a stochastic impulse control problem
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Conference on Numerical Methods in Finance, INRIA Rocquencourt, France, Février, feb, 2006 - Numerical analysis for super-replication problems
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New trends in viscosity solutions and non-linear PDE, Lisboa, Portugal, July 2006, 2006
- An adaptative anti-dissipative method for optimal control problems (poster)
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2nd Congrès National de Mathématiques Appliquées. Evian, may, 2005 - Error estimate for a stochastic impulse control problem
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Conference on Opimization under Uncertainties, Université de Heidelberg, Allemagne, September, 2005 - Error estimates for a stochastic differential game
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22nd IFIP, Conference on System Modeling and Optimization, Ecole Polytechnique de Turin, Italie, Juillet, jul, 2005 - Estimation d'erreur pour un problème de contrôle impulsionnel
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2ème Congrès National des Mathématiques Appliquées, Evian, France, Mai, mai 2005 - Invitation au mini-symposium "Level-set methods, Hamilton-Jacobi equations and applications"
The sixth European Conference on Numerical Mathematics and Advanced Applications (ENUMATH'05), Santiago de Compostele, Spain. July 18-25 2005, jul, 2005 - Méthodes numériques pour les équations HJB Stochastiques
8èmes Journées d'Analyse Numérique et Optimisation (JANO'08), 14-16 Décembre 2005 à Rabat, 2005 - Numerical mathods for HJB equations and error estimates
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Conference on Optimization Frameworks for Industrial Applications, EDF, Paris, France, Octobre, oct, 2005 - Résolution des équations HJB déterministes par le schéma ultrabee sur des grilles adaptatives
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Tendances des mathématiques appliquées en Tunisie, Algérie, Maroc. Tunis, avr 2005 - Ultra bee scheme on adaptative grids. Application to optimal control problems
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22nd IFIP TC 7 Conference on System Modeling and Optimization. Turin, jul, 2005
- Poster: Stochastic differential game: the adverse stopping case
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FGS-2004, Université d'Avignon, France, Septembre, sep, 2004 - Stochastic differential game: the adverse stopping case
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Numerical methods for viscosity solutions and applications, Université La Sapienza, Rome, Italie, Septembre, sep, 2004
- Chaînes de Markov consistantes pour les équations HJB stochastiques. (Conférencier invité)
Colloque PICOF'02 Carthage - Tunisie, 10-12 avril 2002., 2002 - Consistency conditions of Finite Difference Schemes for the Stochastic HJB Equation,
French German Polish Conference on Optimization, Cottbus - September 9-13 2002., sep, 2002
Rapports de recherche
- Couplage des approches HJB et PMP pour une mission de Ariane (GTO)
, , et
Rapport de recherche CNES: RT-NT-431-ZZ-1002-INRI, nov 2010 - Hamilton-Jacobi approach for the climbing problem of multi-stage launchers
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hal-00537649, 2010 [ ] - Optimisation de trajectoire incluant des phases balistiques pour le lanceur Ariane V
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Rapport de recherche CNES: RT-NT-431-ZZ-1001-INRI, pp. 1-- 30, sep, 2010
- Theoretical and numerical study of HJB approach for space launcher problems
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Rapport CNES, RT-NT-4311200-ZZ-805-CNES, pp. 1-33, dec, 2008
- An adaptative antidissipative method for optimal control problems
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Rapport de recherche INRIA, R5770, 2005 - Error estimate for a stochastic impulse control problem
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Rapport de Recherche INRIA, RR-5606, Juin, jun, 2005
- Error estimates for stochastic differential games: the adverse stopping case
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Rapport de recherche INRIA, RR-5441, 2004
Cours
- Optimisation quadratique
et
Cours de 1ère année, 109 pages, ENSTA, 2007
Brevets
- Energy management method for an electric vehicle
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Famille de brevets: EP2790988 (2014-10-22), US2014350763 (2014-11-27), FR2984570 (2013-06-21); WO2013087536 (2013-06-20), 2013 - Method for determining maximum mileage range of electric vehicle, involves determining moment at which state of change of battery tends to zero following evolution of energy state of vehicle along trajectory
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Référence du brevet: FR2988061 (2013-09-20), 2013 - PROCEDE DE GESTION DENERGIE DUN VEHICULE ELECTRIQUE
et
Référence du brevet: FR2988060 (2013-09-20), 2013