retour page principale

Publications

Livres

	E. Trélat. Contrôle optimal : théorie & applications. Vuibert, Collection "Mathématiques Concrètes", 2005, 246 pages. Pdf file, Compressed Ps file. ISBN : 2 7117 7175 X.
	B. Bonnard, L. Faubourg, E. Trélat. Mécanique céleste et contrôle de systèmes spatiaux. Math. & Appl., Vol. 51, Springer Verlag, 2006, XIV, 276 pages. Table des matières. ISBN : 3-540-28373-0.

Chapitres de livres, et éditions d'actes

Y. Chitour, E. Trélat, Controllability of partial differential equations, Advanced Topics in Control Systems Theory, Lecture Notes from FAP 2005, Vol. 328 (2006), F. Lamnabhi-Lagarrigue, A. Loria, E. Panteley (Eds), 171--198. Pdf file, Ps file.
Proceedings of the 13th IFAC Workshop on Control Applications of Optimisation (CAO'06), Internat. J. Tomog. Stat., Special Issues, Vol. 5, 6, and 7 (2007), D. F. M. Torres and E. Trélat (Eds). Pdf file.

Prépublications

M. Cerf, T. Haberkorn, E. Trélat, Continuation from a flat to a round Earth model in the coplanar orbit transfer problem, Preprint Hal (2010), 28 pages. Pdf file.
S. Labbé, Y. Privat, E. Trélat, Stability properties of steady-states for a network of ferromagnetic nanowires, Preprint Hal (2010), 24 pages. Pdf file.
Y. Tan, E. Trélat, Y. Chitour, D. Nesic, Dynamic practical stabilization of sampled-data linear distributed parameter systems, Preprint Hal (2009), 23 pages. Pdf file.

Publications dans des journaux et revues mathématiques

T. Haberkorn, E. Trélat, Convergence results for smooth regularizations of hybrid nonlinear optimal control problems, Preprint Hal (2010), 32 pages, to appear in SIAM J. Control Optim. Pdf file.
G. Archambeau, P. Augros, E. Trélat, Eight-shaped Lissajous orbits in the Earth-Moon system, Preprint Hal (2008), 21 pages, to appear in MathS in Action. Pdf file.
M. Jungers, E. Trélat, H. Abou-Kandil, Min-max and min-min Stackelberg strategies with closed-loop information structure, Preprint Hal (2010), 30 pages, to appear in J. Dynam. Control Systems 17 (2011), no. 3. Pdf file.
C. J. Silva, E. Trélat, Asymptotic approach on conjugate points for minimal time bang-bang controls, Syst. Cont. Letters 59 (2010), 720--733. Pdf file.
C. J. Silva, E. Trélat, Smooth regularization of bang-bang optimal control problems, IEEE Trans. Autom. Control 55 (2010), no. 11, 2488--2499. Pdf file.
M. Bergounioux, E. Trélat, A variational method using fractional order Hilbert spaces for tomographic reconstruction of blurred and noised binary images, J. Funct. Anal. 259 (2010), no. 9, 2296--2332. Pdf file.
L. Rifford, E. Trélat, On the stabilization problem for nonholonomic distributions, J. Eur. Math. Soc. 11 (2009), 223--255. Pdf file.
F. Bonnans, J. Laurent-Varin, P. Martinon, E. Trélat, Numerical study of optimal trajectories with singular arcs for an Ariane 5 launcher, J. Guidance Cont. Dynam. 32 (2009), no. 1, 51--55. Pdf file.
G. Carbou, S. Labbé, E. Trélat, Smooth control of nanowires by means of a magnetic ﬁeld, Comm. Pure Appl. Anal. 8 (2009), no. 3, 871--879. Pdf file.
R. Abraham, M. Bergounioux, E. Trélat, A penalization approach for tomographic reconstruction of binary axially symmetric objects, Applied Math. Optim. 58 (2008), no. 3, 345--371. Pdf file.
F. Bonnans, P. Martinon, E. Trélat, Singular arcs in the generalized Goddard’s Problem, J. Optim. Theory Appl. 139 (2008), no. 2, 439--461. Pdf file.
J.-M. Coron, E. Trélat, R. Vazquez, Control for fast and stable laminar-to-high-Reynolds-numbers transfer in a 2D Navier-Stokes channel flow, Discrete Contin. Dyn. Syst. Ser. B 10 (2008), no. 4, 925--956. Pdf file.
D. Henrion, J.-B. Lasserre, C. Prieur, E. Trélat, Nonlinear optimal control via occupation measures and LMI-relaxations, SIAM J. Control Optim. 47 (2008), no. 4, 1643--1666. Pdf file.
Y. Chitour, F. Jean, E. Trélat, Singular trajectories of control-affine systems, SIAM J. Control Optim. 47 (2008), no. 2, 1078--1095. Pdf file, Ps file.
G. Carbou, S. Labbé, E. Trélat, Control of travelling walls in a ferromagnetic nanowire, Discrete Contin. Dyn. Syst. Ser. S 1 (2008), no. 1, 51--59. Pdf file.
C. Prieur, E. Trélat, On two hybrid robust optimal stabilization problems, Int. J. Tomogr. Stat. 6 (2007), no. S07, 86--91. Pdf file.
B. Bonnard, J.-B. Caillau, E. Trélat, Second order optimality conditions in the smooth case and applications in optimal control, ESAIM Control Optim. Calc. Var. 13 (2007), no. 2, 207--236. Pdf file, Ps file.
C. Prieur, E. Trélat, Hybrid robust stabilization in the Martinet case, Control Cybernet. 35 (2006), no. 4, 923--945. Pdf file, Ps file.
C. Prieur, E. Trélat, Quasi-optimal robust stabilization of control systems, SIAM J. Control Optim. 45 (2006), no. 5, 1875--1897. Pdf file, Ps file.
J.-M. Coron, E. Trélat, Global steady-state stabilization and controllability of 1-D semilinear wave equations, Commun. Contemp. Math. 8 (2006), no. 4, 535--567. Pdf file, Ps file.
S. Labbé, E. Trélat, Uniform controllability of semidiscrete approximations of parabolic control systems, Syst. Cont. Letters 55 (2006), no. 7, 597--609. Pdf file, Ps file.
E. Trélat, Global subanalytic solutions of Hamilton-Jacobi type equations, Ann. Inst. H. Poincaré Anal. Non Linéaire 23 (2006), no. 3, 363--387. Pdf file, Ps file.
Y. Chitour, F. Jean, E. Trélat, Genericity results for singular trajectories, J. Differential Geom. 73 (2006), no. 1, 45--73. Pdf file, Ps file.
E. Trélat, Singular trajectories and subanalyticity in optimal control and Hamilton-Jacobi theory, Rend. Sem. Mat. Univ. Pol. Torino 64 (2006), no. 1, 97--109. Pdf file, Ps file.
M. Schmidt, E. Trélat, Controllability of Couette flows, Comm. Pure Appl. Anal. 5 (2006), no. 1, 201--211. Pdf file, Ps file.
B. Bonnard, J.-B. Caillau, E. Trélat, Geometric optimal control of elliptic Keplerian orbits, Discrete Contin. Dyn. Syst. Ser. B 5 (2005), no. 4, 929--956. Pdf file, Ps file.
C. Prieur, E. Trélat, Robust optimal stabilization of the Brockett integrator via a hybrid feedback, Math. Control Signals Systems 17 (2005), no. 3, 201--216. Pdf file, Ps file.
L. Rifford, E. Trélat, Morse-Sard type results in sub-Riemannian geometry, Math. Ann. 332 (2005), no. 1, 145--159. Pdf file, Ps file.
B. Bonnard, L. Faubourg, E. Trélat, Optimal control of the atmospheric arc of a space shuttle and numerical simulations by multiple shooting-technique, Math. Models Methods Applied Sci. 15 (2005), no. 1, 109--140. Pdf file, Ps file.
J.-M. Coron, E. Trélat, Global steady-state controllability of 1-D semilinear heat equations, SIAM J. Control Optim. 43 (2004), no. 2, 549--569. Pdf file, Ps file.
E. Trélat, Solutions sous-analytiques globales de certaines équations d'Hamilton-Jacobi, C. R. Math. Acad. Sci. Paris 337 (2003), no. 10, 653--656. Pdf file, Ps file.
E. Trélat, Optimal control of a space shuttle, and numerical simulations, Discrete Contin. Dyn. Syst. (2003), suppl., 842--851. Pdf file, Ps file.
Y. Chitour, F. Jean, E. Trélat, Propriétés génériques des trajectoires singulières, C. R. Math. Acad. Sci. Paris 337 (2003), no. 1, 49--52. Pdf file, Ps file.
B. Bonnard, L. Faubourg, G. Launay, E. Trélat, Optimal control with state constraints and the space shuttle re-entry problem, J. Dynam. Control Syst. 9 (2003), no. 2, 155--199. Pdf file, Ps file.
B. Bonnard, E. Trélat, Une approche géométrique du contrôle optimal de l'arc atmosphérique de la navette spatiale, ESAIM Cont. Opt. Calc. Var. 7 (2002), 179--222. Pdf file, Ps file.
B. Bonnard, E. Trélat, On the role of abnormal minimizers in SR-geometry, Ann. Fac. Sci. Toulouse (6) 10 (2001), no. 3, 405--491. Pdf file, Compressed Ps file.
E. Trélat, Non subanalyticity of sub-Riemannian Martinet spheres, C. R. Acad. Sci. Paris Ser. I Math. 332 (2001), no. 6, 527--532. Pdf file, Ps file.
E. Trélat, Asymptotics of accessibility sets along an abnormal trajectory, ESAIM Control Optim. Calc. Var. 6 (2001), 387--414. Pdf file, Ps file.
B. Bonnard, G. Launay, E. Trélat, The transcendence needed to compute the sphere and wave front in Martinet SR-geometry, J. Math. Sci., New York 103 (2001), no. 6, 686--708. Pdf file, Ps file.
E. Trélat, Some properties of the value function and its level sets for affine control systems with quadratic cost, J. Dynam. Control Systems 6 (2000), no. 4, 511--541. Pdf file, Ps file.
B. Bonnard, M. Chyba, E. Trélat, Sub-Riemannian geometry : one-parameter deformation of the Martinet flat case, J. Dyn. Control Systems 4 (1998), no. 1, 59--76. Pdf file, Ps file.

Actes de colloque, proceedings

Y. Tan, E. Trélat, Y. Chitour, D. Nesic, Dynamic practical stabilization of sampled-data linear distributed parameter systems, Proceedings 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference, Shanghai (2009), 8 pages. Pdf file.
M. Jungers, E. Trélat, H. Abou-Kandil, A Stackelberg Game Approach to Mixed $H_2/H_\infty$ Control, Proceedings of 17th IFAC World Congress, Seoul, Korea (2008), 15 pages. Pdf file.
B. Bonnard, J.-B. Caillau, E. Trélat, Second order optimality conditions with applications, Discrete Contin. Dyn. Syst. (2007), Dynamical Systems and Differential Equations, Proceedings of the 6th AIMS International Conference, suppl., 145--154. Pdf file.
M. Jungers, E. Trélat, H. Abou-Kandil, Commande mixte $H_2/H_\infty$ : une approche par la stratégie de Stackelberg, J. Europ. Syst. Autom., No. spécial "La synthèse multi-objectifs", Vol. 40 (2006), no. 9-10, 1113--1139. Pdf file.
J.-M. Coron, E. Trélat, R. Vazquez, Fast tracking of Poiseuille trajectories in Navier-Stokes 2D channel flow, Taming heterogeneity and complexity of embedded control, 699--720, ISTE, London, 2007. Pdf file.
J.-M. Coron, E. Trélat, R. Vazquez, Stable Poiseuille flow transfer for a Navier-Stokes system, Proceedings of 2006 American Control Conference (ACC 2006), Minneapolis, 6 pages. Pdf file.
Y. Chitour, F. Jean, E. Trélat, Singular trajectories of driftless and control-affine systems, Proceedings CDC-ECC'05, Séville, Spain (2005), 6 pages. Pdf file, Ps file.
C. Prieur, E. Trélat, Semi-global minimal time hybrid robust stabilization of analytic driftless control-affine systems, Proceedings CDC-ECC'05, Séville, Spain (2005), 6 pages. Pdf file, Ps file.
B. Bonnard, J.-B. Caillau, E. Trélat, Computation of conjugate times in smooth optimal control: the COTCOT algorithm, Proceedings CDC-ECC'05, Séville, Spain (2005), 6 pages. Pdf file.
J.-M. Coron, E. Trélat, Feedback stabilization along a path of steady-states for 1-D semilinear heat and wave equations, Proceedings CDC-ECC'05, Séville, Spain (2005), 6 pages. Pdf file, Ps file.
B. Bonnard, J.-B. Caillau, E. Trélat, Geometric analysis of minimum time Keplerian orbit transfers, Proceedings of the 22nd IFIP TC 7 Conference on System Modeling and Optimization, Torino, Italy, Springer (2006), 6 pages. Pdf file.
E. Trélat, Contrôle optimal appliqué au problème de rentrée atmosphérique, Proceedings, Conférence Internationale Francophone d'Automatique (CIFA 2004), Douz, Tunisie, e-STA (Sciences et Technologies de l'Automatique) 1, 4 (2004), 6 pages. Pdf file, Ps file.
C. Prieur, E. Trélat, Robust optimal stabilization of the Brockett integrator via a hybrid feedback, Proceedings of the Sixteenth International Symposium on Mathematical Theory of Networks and Systems (MTNS 2004), 6 pages. Pdf file, Ps file.
B. Bonnard, L. Faubourg, E. Trélat, Conjugate times for smooth singular trajectories and bang-bang extremals, Lagrangian and Hamiltonian methods for nonlinear control 2003, 177--182, IFAC, Laxenburg, 2003. Pdf file, Ps file.
B. Bonnard, L. Faubourg, E. Trélat, Classification of local optimal syntheses for time minimal control problems with state constraints, Lagrangian and Hamiltonian methods for nonlinear control 2003, 117--122, IFAC, Laxenburg, 2003. Pdf file, Ps file.
E. Trélat, Bifurcations of reachable sets near an abnormal direction and consequences, Dynamics, bifurcations, and control (Kloster Irsee, 2001), Lecture Notes in Control and Inform. Sci. 273, Springer, Berlin (2002), 89--99. Pdf file, Ps file.
E. Trélat, Optimality of singular trajectories and asymptotics of accessibility sets under generic assumptions, Contemporary Trends in Nonlinear Geometric Control Theory and its Applications (Mexico City 2000), World Sci. Publishing, River Edge, NJ, 2002. Pdf file, Ps file.
B. Bonnard, E. Trélat, Stratification du secteur anormal dans la sphère de Martinet de petit rayon, Nonlinear Control in the Year 2000, Vol. 1 (Paris), 239--251, Lecture Notes in Control and Inform. Sci. 259, Springer, London, 2001. Pdf file, Ps file.
B. Bonnard, G. Launay, E. Trélat, The transcendence required for computing the sphere and wave front in the Martinet SR-geometry, (Russian) Geometric control theory (Moscow, 1998), 82--117, Itogi Nauki Tekh. Ser. Sovrem. Mat. Prilozh. Temat. Obz. 64 (1999). Vseross. Inst. Nauchn. i Tekhn. Inform. (VINITI), Moscow, 1999.

Articles de vulgarisation

E. Trélat, Théorie du contrôle, points de Lagrange, et exploration spatiale, Images des Mathématiques, CNRS (2010). Link.
E. Trélat, A la conquête des points de Lagrange, Microscoop Hors Série 18 (2009), 24--25. Pdf file.
C. J. Silva, D. F. M. Torres, E. Trélat, O controlo optimo e as suas multiplas aplicações, Bol. Soc. Port. Mat. 61 (2009), 11--37. Pdf file.
E. Trélat, Théorie du contrôle: contrôle optimal et stabilisation, Microscoop 55 (2008), 14--15. Pdf file.
J.-M. Coron, E. Trélat, Tout est sous contrôle, Matapli 83 (2007), 59--73. Pdf file.
J.-M. Coron, E. Trélat, Tout est sous contrôle, Plein Sud - Spécial Recherche (2004), 126--131. Pdf file.
E. Trélat, Introduction au contrôle optimal, Revue de Math. Spé, Math. Concrètes 3 (2002/2003). Pdf file, Ps file.
E. Trélat, Contrôle optimal et stabilisation d'une navette spatiale. Pdf file, Ps file.

Rapports techniques

B. Bonnard, J.-B. Caillau, E. Trélat, COTCOT: short reference manual, Technical report RT/APO/05/1, http://apo.enseeiht.fr/cotcot/. Pdf file.

Thèse de doctorat

Etude asymptotique et transcendance de la fonction valeur en contrôle optimal ; catégorie log-exp en géométrie sous-Riemannienne dans le cas Martinet.
Soutenue le 13 décembre 2000, Mention Très honorable (Univ. Bourgogne).
Jury de thèse : R. Roussarie (président), J.-M. Coron, K. Kurdyka (rapporteurs), A. Agrachev, B. Bonnard, J. P. Gauthier, A. Jourani, I. Kupka (examinateurs). Pdf file, Ps file.

Habilitation à diriger des recherches

Contrôle en dimension finie et infinie.
Soutenue le 25 novembre 2005 (Labo. Math., Univ. Paris-Sud).
Jury : H. Abou-Kandil, A. Agrachev (rapporteur), G. Bastin, B. Bonnard, J.-M. Coron, P. Rouchon, M. Tucsnak (rapporteur). Pdf file, Ps file.