EN FR
EN FR


previous Previous | up Home


Bibliography

Publications of the year

Doctoral Dissertations and Habilitation Theses

Articles in International Peer-Reviewed Journals

  • 2B. Bonnard, M. Claeys, O. Cots, P. Martinon.

    Geometric and numerical methods in the contrast imaging problem in nuclear magnetic resonance, in: Acta Applicandae Mathematicae, February 2015, vol. 135, no 1, pp. 5-45. [ DOI : 10.1007/s10440-014-9947-3 ]

    https://hal.inria.fr/hal-00867753
  • 3B. Bonnard, T. Combot, L. Jassionnesse.

    Integrability methods in the time minimal coherence transfer for Ising chains of three spins, in: Discrete and Continuous Dynamical Systems - Series A (DCDS-A), September 2015, vol. 35, no 9, pp. 4095-4114, 20 pages. [ DOI : 10.3934/dcds.2015.35.4095 ]

    https://hal.archives-ouvertes.fr/hal-00969285
  • 4B. Bonnard, H. Henninger, J. Nemcova, J.-B. Pomet.

    Time Versus Energy in the Averaged Optimal Coplanar Kepler Transfer towards Circular Orbits, in: Acta Applicandae Mathematicae, February 2015, vol. 135, no 2, pp. 47-80. [ DOI : 10.1007/s10440-014-9948-2 ]

    https://hal.inria.fr/hal-00918633
  • 5J.-B. Caillau, Z. Chen, Y. Chitour.

    L 1 -minimization for mechanical systems, in: SIAM Journal on Control and Optimization, 2016.

    https://hal.archives-ouvertes.fr/hal-01136676
  • 6J.-B. Caillau, L. Grüne, M. D. R. De Pinho, E. Trélat, H. Zidani.

    Special issue on New trends in optimal control, in: Discrete and Continuous Dynamical Systems - Series A, September 2015, vol. 35, no 9.

    https://hal.archives-ouvertes.fr/hal-01277412
  • 7G. Contreras, A. Figalli, L. Rifford.

    Generic hyperbolicity of Aubry sets on surfaces, in: Inventiones Mathematicae, 2015, vol. 200, no 1.

    https://hal.archives-ouvertes.fr/hal-00935976
  • 8A. Figalli, T. Gallouët, L. Rifford.

    On the convexity of injectivity domains on nonfocal manifolds, in: SIAM J. Math. Anal., 2015, vol. 47, no 2, pp. 969–1000.

    https://hal.inria.fr/hal-00968354
  • 9A. Figalli, L. Rifford.

    Closing Aubry sets I, in: Communications on Pure and Applied Mathematics, 2015, vol. 68, no 2.

    https://hal.archives-ouvertes.fr/hal-00935965
  • 10A. Figalli, L. Rifford.

    Closing Aubry sets II, in: Communications on Pure and Applied Mathematics, 2015, vol. 68, no 3.

    https://hal.archives-ouvertes.fr/hal-00935970

Scientific Books (or Scientific Book chapters)

  • 11B. Bonnard, M. Chyba, J. Rouot.

    Working Examples In Geometric Optimal Control, Springer, November 2015.

    https://hal.inria.fr/hal-01226734
  • 12B. Bonnard, M. Chyba.

    Singular trajectories in optimal control, in: Encyclopedia of Systems and Control, J. Baillieul, T. Samad (editors), Springer, February 2015.

    https://hal.inria.fr/hal-00939089
  • 13B. Bonnard, H. Henninger, J. Rouot.

    Lunar perturbation of the metric associated to the averaged orbital transfer, in: Analysis and geometry in control theory and its applications, 2015. [ DOI : 10.1007/978-3-319-06917-3_3 ]

    https://hal.inria.fr/hal-01090977
  • 14J.-B. Caillau, M. D. R. De Pinho, L. Grüne, E. Trélat, H. Zidani.

    New Trends for Optimal Control and Sensitivity Analysis, Discrete ad Continous Dynamical Systems - Serie A, AIMS, 2015, vol. 35, no 9. [ DOI : 10.3934/dcds.2015.35.9i ]

    https://hal.inria.fr/hal-01149981
  • 15J.-B. Caillau, A. Farrés.

    On local optima in minimum time control of the restricted three-body problem, Springer, April 2016, vol. Mathematics for Industry. [ DOI : 10.1007/978-3-319-27464-5 ]

    https://hal.archives-ouvertes.fr/hal-01260120
  • 16T. Combot, D. J. Scheeres, A. Farrés, À. Jorba, T. Haberkorn, R. Jedicke, M. Chyba, R. Epenoy, G. Patterson, G. Picot, J.-B. Caillau.

    M. C. Bernard Bonnard (editor), Celestial and Space Mechanics, Celestial and Space Mechanics, Springer, December 2015, 316 p.

    https://hal.archives-ouvertes.fr/hal-01220278

Other Publications

  • 17P. Bettiol, B. Bonnard, L. Giraldi, P. Martinon, J. Rouot.

    The Purcell Three-link swimmer: some geometric and numerical aspects related to periodic optimal controls, October 2015, working paper or preprint.

    https://hal.inria.fr/hal-01143763
  • 18B. Bonnard, M. Chyba, J. Rouot, D. Takagi, R. Zou.

    Optimal Strokes : a Geometric and Numerical Study of the Copepod Swimmer, January 2016, working paper or preprint.

    https://hal.inria.fr/hal-01162407
  • 19L. Giraldi, J.-B. Pomet.

    Local controllability of the two-link magneto-elastic swimmer, April 2015, working paper or preprint.

    https://hal.archives-ouvertes.fr/hal-01145537
References in notes
  • 20A. Agrachev, P. W. Y. Lee.

    Optimal transportation under nonholonomic constraints, in: Trans. Amer. Math. Soc., 2009, vol. 361, no 11, pp. 6019–6047.

    http://dx.doi.org/10.1090/S0002-9947-09-04813-2
  • 21A. Agrachev, P. W. Y. Lee.

    Generalized Ricci Curvature Bounds for Three Dimensional Contact Subriemannian manifold, arXiv, 2011, no arXiv:0903.2550 [math.DG], 3rd version.

    http://arxiv.org/abs/0903.2550
  • 22A. Agrachev, Y. L. Sachkov.

    Control theory from the geometric viewpoint, Encyclopaedia of Mathematical Sciences, Springer-Verlag, Berlin, 2004, vol. 87, xiv+412 p, Control Theory and Optimization, II.
  • 23L. Ambrosio, S. Rigot.

    Optimal mass transportation in the Heisenberg group, in: J. Funct. Anal., 2004, vol. 208, no 2, pp. 261–301.

    http://dx.doi.org/10.1016/S0022-1236(03)00019-3
  • 24V. I. Arnold.

    Mathematical methods of classical mechanics, Graduate Texts in Mathematics, 2nd, Springer-Verlag, New York, 1989, vol. 60, xvi+508 p, Translated from the Russian by K. Vogtmann and A. Weinstein.
  • 25Z. Artstein.

    Stabilization with relaxed control, in: Nonlinear Analysis TMA, November 1983, vol. 7, no 11, pp. 1163-1173.
  • 26A. Bombrun, J.-B. Pomet.

    The averaged control system of fast oscillating control systems, in: SIAM J. Control Optim., 2013, vol. 51, no 3, pp. 2280-2305. [ DOI : 10.1137/11085791X ]

    http://hal.inria.fr/hal-00648330/
  • 27B. Bonnard, J.-B. Caillau.

    Riemannian metric of the averaged energy minimization problem in orbital transfer with low thrust, in: Ann. Inst. H. Poincaré Anal. Non Linéaire, 2007, vol. 24, no 3, pp. 395–411.
  • 28B. Bonnard, J.-B. Caillau.

    Geodesic flow of the averaged controlled Kepler equation, in: Forum Mathematicum, September 2009, vol. 21, no 5, pp. 797–814.

    http://dx.doi.org/10.1515/FORUM.2009.038
  • 29B. Bonnard, M. Chyba.

    Singular trajectories and their role in control theory, Mathématiques & Applications, Springer-Verlag, Berlin, 2003, vol. 40, xvi+357 p.
  • 30B. Bonnard, O. Cots, S. J. Glaser, M. Lapert, D. Sugny, Y. Zhang.

    Geometric Optimal Control of the Contrast Imaging Problem in Nuclear Magnetic Resonance, in: IEEE Transactions on Automatic Control, August 2012, vol. 57, no 8, pp. 1957-1969. [ DOI : 10.1109/TAC.2012.2195859 ]

    http://hal.archives-ouvertes.fr/hal-00750032/
  • 31B. Bonnard, N. Shcherbakova, D. Sugny.

    The smooth continuation method in optimal control with an application to quantum systems, in: ESAIM Control Optim. Calc. Var., 2011, vol. 17, no 1, pp. 267–292.

    http://dx.doi.org/10.1051/cocv/2010004
  • 32B. Bonnard, D. Sugny.

    Time-minimal control of dissipative two-level quantum systems: the integrable case, in: SIAM J. Control Optim., 2009, vol. 48, no 3, pp. 1289–1308.

    http://dx.doi.org/10.1137/080717043
  • 33B. Bonnard, D. Sugny.

    Optimal control with applications in space and quantum dynamics, vol. 5 of AIMS Series on Applied Mathematics, American Institute of Mathematical Sciences, Springfield, MO, 2012, xvi+283 p.
  • 34U. Boscain, B. Piccoli.

    Optimal syntheses for control systems on 2-D manifolds, Mathématiques & Applications (Berlin) [Mathematics & Applications], Springer-Verlag, Berlin, 2004, vol. 43, xiv+261 p.
  • 35Y. Brenier.

    Polar factorization and monotone rearrangement of vector-valued functions, in: Comm. Pure Appl. Math., 1991, vol. 44, no 4, pp. 375–417.

    http://dx.doi.org/10.1002/cpa.3160440402
  • 36F. Chaplais.

    Averaging and deterministic optimal control, in: SIAM J. Control Optim., 1987, vol. 25, no 3, pp. 767–780.
  • 37J. C. Doyle, B. A. Francis, A. R. Tannenbaum.

    Feedback control theory, Macmillan Publishing Company, New York, 1992, xii+227 p.
  • 38A. Figalli, L. Rifford.

    Mass transportation on sub-Riemannian manifolds, in: Geom. Funct. Anal., 2010, vol. 20, no 1, pp. 124–159.

    http://dx.doi.org/10.1007/s00039-010-0053-z
  • 39M. Fliess, J. Lévine, P. Martin, P. Rouchon.

    Flatness and Defect of Nonlinear Systems: Introductory Theory and Examples, in: Internat. J. Control, 1995, vol. 61, no 6, pp. 1327-1361.

    http://cas.ensmp.fr/%7Erouchon/publications/PR1995/IJC95.pdf
  • 40S. Geffroy.

    Généralisation des techniques de moyennation en contrôle optimal - Application aux problèmes de rendez-vous orbitaux en poussée faible, Institut National Polytechnique de Toulouse, Toulouse, France, October 1997.
  • 41A. Isidori.

    Nonlinear Control Systems, Comm. in Control Engineering, 3rd, Springer-Verlag, 1995.
  • 42L. Jassionnesse.

    Optimal control and Clairaut-Liouville metrics with applications, Université de Bourgogne, November 2014.

    https://tel.archives-ouvertes.fr/tel-01131399
  • 43N. Juillet.

    Geometric inequalities and generalized Ricci bounds in the Heisenberg group, in: Int. Math. Res. Not. IMRN, 2009, vol. 13, pp. 2347–2373.
  • 44V. Jurdjevic.

    Non-Euclidean elastica, in: Amer. J. Math., 1995, vol. 117, no 1, pp. 93–124.

    http://dx.doi.org/10.2307/2375037
  • 45T. Kailath.

    Linear systems, Information and System Sciences, Prentice-Hall Inc., Englewood Cliffs, N.J., 1980.
  • 46L. V. Kantorovich.

    On a problem of Monge, in: Uspekhi mat. Nauka, 1948, vol. 3, pp. 225–226, English translation in J. Math. Sci. (N. Y.) 133 (2006), 1383–1383.

    http://dx.doi.org/10.1007/s10958-006-0050-9
  • 47W. Klingenberg.

    Lectures on closed geodesics, Grundlehren der Mathematischen Wissenschaften, Springer-Verlag, Berlin, 1978, vol. 230, x+227 p.
  • 48W. Klingenberg, F. Takens.

    Generic properties of geodesic flows, in: Math. Ann., 1972, vol. 197, pp. 323–334.
  • 49E. B. Lee, L. Markus.

    Foundations of optimal control theory, John Wiley & Sons Inc., New York, 1967.
  • 50J. Lott, C. Villani.

    Ricci curvature for metric-measure spaces via optimal transport, in: Ann. of Math. (2), 2009, vol. 169, no 3, pp. 903–991.

    http://dx.doi.org/10.4007/annals.2009.169.903
  • 51P. Martin, R. M. Murray, P. Rouchon.

    Flat systems, in: Mathematical control theory, Part 1, 2 (Trieste, 2001), ICTP Lect. Notes, VIII, Abdus Salam Int. Cent. Theoret. Phys., Trieste, 2002, pp. 705–768.

    http://users.ictp.it/~pub_off/lectures/lns008/Rouchon/Rouchon.pdf
  • 52R. J. McCann.

    Polar factorization of maps on Riemannian manifolds, in: Geom. Funct. Anal., 2001, vol. 11, no 3, pp. 589–608.

    http://dx.doi.org/10.1007/PL00001679
  • 53G. Monge.

    Mémoire sur la théorie des déblais et des remblais, in: Histoire de l'Académie Royale des Sciences, 1781, pp. 666-704.

    http://gallica.bnf.fr/ark:/12148/bpt6k35800.image.f796
  • 54J.-M. Morel, F. Santambrogio.

    Comparison of distances between measures, in: Appl. Math. Lett., 2007, vol. 20, no 4, pp. 427–432.

    http://dx.doi.org/10.1016/j.aml.2006.05.009
  • 55Q. Mérigot.

    Détection de structure géométrique dans les nuages de points, Univ. de Nice Sophia Antipolis, 2009.

    http://tel.archives-ouvertes.fr/tel-00443038/
  • 56L. S. Pontryagin, V. G. Boltjanskiĭ, R. V. Gamkrelidze, E. Mitchenko.

    Théorie mathématique des processus optimaux, Editions MIR, Moscou, 1974.
  • 57J. A. Sanders, F. Verhulst.

    Averaging Methods in Nonlinear Dynamical Systems, Applied Mathematical Sciences, Springer-Verlag, 1985, vol. 56.
  • 58K.-T. Sturm.

    On the geometry of metric measure spaces. I, in: Acta Math., 2006, vol. 196, no 1, pp. 65–131.

    http://dx.doi.org/10.1007/s11511-006-0002-8
  • 59K.-T. Sturm.

    On the geometry of metric measure spaces. II, in: Acta Math., 2006, vol. 196, no 1, pp. 133–177.

    http://dx.doi.org/10.1007/s11511-006-0003-7


previous Previous | up Home