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Bibliography

Publications of the year

Doctoral Dissertations and Habilitation Theses

Articles in International Peer-Reviewed Journals

  • 2B. Bonnard, J.-B. Caillau.

    Metrics with equatorial singularities on the sphere, in: Ann. Mat. Pura Appl., 2014, vol. 193, no 5, pp. 1353-1382. [ DOI : 10.1007/s10231-013-0333-y ]

    https://hal.archives-ouvertes.fr/hal-00319299
  • 3B. Bonnard, M. Claeys, O. Cots, P. Martinon.

    Geometric and numerical methods in the contrast imaging problem in nuclear magnetic resonance, in: Acta Applicandae Mathematicae, June 2014, vol. 135, no 1, pp. 5-45. [ DOI : 10.1007/s10440-014-9947-3 ]

    https://hal.inria.fr/hal-00867753
  • 4B. Bonnard, O. Cots.

    Geometric numerical methods and results in the control imaging problem in nuclear magnetic resonance, in: Mathematical Models and Methods in Applied Sciences, 2014, vol. 24, no 1, pp. 187-212. [ DOI : 10.1142/S0218202513500504 ]

    https://hal.inria.fr/hal-00939153
  • 5B. Bonnard, O. Cots, J.-B. Pomet, N. Shcherbakova.

    Riemannian metrics on 2D-manifolds related to the Euler-Poinsot rigid body motion, in: ESAIM Control Optim. Calc. Var., 2014, forthcoming.

    https://hal.inria.fr/hal-00918587
  • 6B. 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, 2015, vol. 135, pp. 47-80. [ DOI : 10.1007/s10440-014-9948-2 ]

    https://hal.inria.fr/hal-00918633

International Conferences with Proceedings

  • 7B. Bonnard, H. Henninger, J.-B. Pomet.

    Time minimization versus energy minimization in the one-input controlled Kepler problem with weak propulsion, in: 21st International Symposium on Mathematical Theory of Networks and Systems, Groningen, Netherlands, July 2014, pp. 686-688.

    https://hal.inria.fr/hal-01112429

Scientific Books (or Scientific Book chapters)

  • 8B. 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
  • 9L. Rifford.

    Sub-Riemannian Geometry and Optimal Transport, SpringerBriefs in Mathematics, Springer International Publishing, 2014. [ DOI : 10.1007/978-3-319-04804-8 ]

    https://hal.inria.fr/hal-01131787

Other Publications

References in notes
  • 16A. Agrachev, P. W. Y. Lee.

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

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  • 17A. 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
  • 18A. 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.
  • 19L. Ambrosio, S. Rigot.

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  • 21Z. Artstein.

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  • 22A. 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/
  • 23B. 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.
  • 24B. 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
  • 25B. Bonnard, J.-B. Caillau, R. Sinclair, M. Tanaka.

    Conjugate and cut loci of a two-sphere of revolution with application to optimal control, in: Ann. Inst. H. Poincaré Anal. Non Linéaire, 2009, vol. 26, no 4, pp. 1081–1098.

    http://dx.doi.org/10.1016/j.anihpc.2008.03.010
  • 26B. Bonnard, M. Chyba.

    Singular trajectories and their role in control theory, Mathématiques & Applications, Springer-Verlag, Berlin, 2003, vol. 40, xvi+357 p.
  • 27B. 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/
  • 28B. 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
  • 29B. 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
  • 30B. 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.
  • 31U. 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.
  • 32Y. 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
  • 33F. Chaplais.

    Averaging and deterministic optimal control, in: SIAM J. Control Optim., 1987, vol. 25, no 3, pp. 767–780.
  • 34F. H. Clarke, Y. S. Ledyaev, L. Rifford, R. J. Stern.

    Feedback stabilization and Lyapunov functions, in: SIAM J. Control Optim., 2000, vol. 39, no 1, pp. 25–48.

    http://dx.doi.org/10.1137/S0363012999352297
  • 35J. C. Doyle, B. A. Francis, A. R. Tannenbaum.

    Feedback control theory, Macmillan Publishing Company, New York, 1992, xii+227 p.
  • 36L. Faubourg, J.-B. Pomet.

    Control Lyapunov functions for homogeneous "Jurdjevic-Quinn” systems, in: ESAIM Control Optim. Calc. Var., 2000, vol. 5, pp. 293-311.

    http://www.edpsciences.org/cocv/
  • 37A. 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
  • 38A. Figalli, L. Rifford.

    Closing Aubry sets II, in: Communications on Pure and Applied Mathematics, 2015, vol. 68, no 3, pp. 345-412.

    https://hal.archives-ouvertes.fr/hal-00935970
  • 39A. Figalli, L. Rifford.

    Closing Aubry sets I, in: Communications on Pure and Applied Mathematics, 2015, vol. 68, no 2, pp. 210-285.

    https://hal.archives-ouvertes.fr/hal-00935965
  • 40M. 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://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.66.8871
  • 41S. 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.
  • 42A. Isidori.

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

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  • 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.

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  • 48W. Klingenberg, F. Takens.

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  • 49E. B. Lee, L. Markus.

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  • 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.

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  • 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.

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  • 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
  • 55P. Morin, J.-B. Pomet, C. Samson.

    Design of Homogeneous Time-Varying Stabilizing Control Laws for Driftless Controllable Systems Via Oscillatory Approximation of Lie Brackets in Closed Loop, in: SIAM J. Control Optim., 1999, vol. 38, no 1, pp. 22-49.

    http://dx.doi.org/10.1137/S0363012997315427
  • 56Q. Mérigot.

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

    http://tel.archives-ouvertes.fr/tel-00443038/
  • 57J.-B. Pomet.

    Explicit Design of Time-Varying Stabilizing Control Laws for a Class of Controllable Systems without Drift, in: Syst. & Control Lett., 1992, vol. 18, pp. 147-158.
  • 58L. S. Pontryagin, V. G. Boltjanskiĭ, R. V. Gamkrelidze, E. Mitchenko.

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  • 59L. Rifford.

    On the existence of nonsmooth control-Lyapunov functions in the sense of generalized gradients, in: ESAIM Control Optim. Calc. Var., 2001, vol. 6, pp. 593–611.

    http://dx.doi.org/10.1051/cocv:2001124
  • 60L. Rifford.

    On the existence of local smooth repulsive stabilizing feedbacks in dimension three, in: J. Differential Equations, 2006, vol. 226, no 2, pp. 429–500.

    http://dx.doi.org/10.1016/j.jde.2005.10.017
  • 61L. Rifford, R. O. Ruggiero.

    Generic Properties of Closed Orbits of Hamiltonian Flows from Mañé's Viewpoint, in: International Mathematics Research Notices, 2012. [ DOI : 10.1093/imrn/rnr231 ]

    http://imrn.oxfordjournals.org/content/early/2011/12/14/imrn.rnr231.abstract
  • 62J. A. Sanders, F. Verhulst.

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  • 63K.-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
  • 64K.-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


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