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Bibliography

Publications of the year

Articles in International Peer-Reviewed Journals

  • 1A. Bombrun, J.-B. Pomet.

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

    http://hal.inria.fr/hal-00648330
  • 2B. Bonnard, J.-B. Caillau.

    Metrics with equatorial singularities on the sphere, in: Ann. Mat. Pura Appl., 2014, (to appear). [ DOI : 10.1007/s10231-013-0333-y ]

    http://hal.inria.fr/hal-00319299
  • 3B. Bonnard, J.-B. Caillau, G. Janin.

    Conjugate-cut loci and injectivity domains on two-spheres of revolution, in: ESAIM Control Optim. and Calc. Var., 2013, vol. 19, no 2, pp. 533-554.

    http://hal.inria.fr/hal-00802078
  • 4B. Bonnard, M. Chyba, J. Marriott.

    Feedback equivalence and the contrast problem in nuclear magnetic resonance imaging, in: Pacific Journal of Optimization, 2013, vol. 9, pp. 635-650.

    http://hal.inria.fr/hal-00939498
  • 5B. Bonnard, M. Chyba, J. Marriott.

    Singular Trajectories and the Contrast Imaging Problem in Nuclear Magnetic Resonance, in: SIAM Journal on Control and Optimization, 2013, vol. 51, no 2, pp. 1325-1349. [ DOI : 10.1137/110833427 ]

    http://hal.inria.fr/hal-00939496
  • 6B. 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. [ DOI : 10.1142/S0218202513500504 ]

    http://hal.inria.fr/hal-00939153
  • 7B. 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, to appear.

    http://hal.inria.fr/hal-00918587
  • 8B. Bonnard, O. Cots, N. Shcherbakova.

    Energy Minimization Problem in Two-Level Dissipative Quantum Control: Meridian Case, in: Journal of Mathematical Sciences, 2013, vol. 195, no 3, pp. 311-335. [ DOI : 10.1007/s10958-013-1582-4 ]

    http://hal.inria.fr/hal-00939131
  • 9B. Bonnard, O. Cots, N. Shcherbakova.

    The Serret-Andoyer Riemannian metric and Euler-Poinsot rigid body motion, in: Mathematical Control and Related Fields, 2013, vol. vol. 3, pp. 287-302. [ DOI : 10.3934/mcrf.2013.3.287 ]

    http://hal.inria.fr/hal-00908905
  • 10B. Bonnard, A. Jacquemard, M. Chyba, J. Marriott.

    Algebraic geometric classification of the singular flow in the contrast imaging problem in nuclear magnetic resonance, in: Mathematical Control and Related Fields, 2013, vol. 3, no 4, pp. 397-432. [ DOI : 10.3934/mcrf.2013.3.397 ]

    http://hal.inria.fr/hal-00939495
  • 11L. Rifford.

    Ricci curvature in Carnot groups, in: Mathematical Control and Related Fields, 2013, vol. 3, no 4, 467 p.

    http://hal.inria.fr/hal-00923326

International Conferences with Proceedings

  • 12B. Bonnard, M. Claeys, O. Cots, P. Martinon.

    Comparison of Numerical Methods in the Contrast Imaging Problem in NMR, in: 52nd IEEE Conference on Decision and Control, Firenze, Italy, December 2013.

    http://hal.inria.fr/hal-00800436
  • 13B. Bonnard, O. Cots, N. Shcherbakova.

    Riemannian metrics on 2D manifolds related to the Euler-Poinsot rigid body problem, in: CDC - 52-nd IEEE Conference on Control Decis., Florence, Italy, 2013.

    http://hal.inria.fr/hal-00925078

Other Publications

  • 14B. Bonnard, M. Chyba.

    Two applications of geometric optimal control to the dynamics of spin particle, 2013, To appear in a volume of "Math and Industry", Springer-Verlag.

    http://hal.inria.fr/hal-00956828
  • 15B. Bonnard, M. Claeys, O. Cots, P. Martinon.

    Geometric and numerical methods in the contrast imaging problem in nuclear magnetic resonance, September 2013.

    http://hal.inria.fr/hal-00867753
  • 16B. Bonnard, H. Henninger, J. Nemcova, J.-B. Pomet.

    Time Versus Energy in the Averaged Optimal Coplanar Kepler Transfer towards Circular Orbits, 2013, Submitted to Acta Applicandae Mathematicae.

    http://hal.inria.fr/hal-00918633
  • 17G. Contreras, A. Figalli, L. Rifford.

    Generic hyperbolicity of Aubry sets on surfaces, 2013.

    http://hal.inria.fr/hal-00935976
  • 18A. Lazrag.

    A geometric control proof of linear Franks' lemma for geodesic flows, 2014.

    http://hal.inria.fr/hal-00939982
References in notes
  • 19A. 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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  • 20A. 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.

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  • 21A. Agrachev, Y. L. Sachkov.

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  • 22L. Ambrosio, S. Rigot.

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  • 25B. 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.
  • 26B. 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
  • 27B. Bonnard, J.-B. Caillau, L. Rifford.

    Convexity of injectivity domains on the ellipsoid of revolution: the oblate case, in: C. R. Math. Acad. Sci. Paris, 2010, vol. 348, no 23-24, pp. 1315–1318.

    http://dx.doi.org/10.1016/j.crma.2010.10.036
  • 28B. Bonnard, M. Chyba.

    Singular trajectories and their role in control theory, Mathématiques & Applications, Springer-Verlag, Berlin, 2003, vol. 40, xvi+357 p.
  • 29B. 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/
  • 30B. 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
  • 31B. 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
  • 32B. 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.
  • 33U. 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.
  • 34Y. 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
  • 35F. Chaplais.

    Averaging and deterministic optimal control, in: SIAM J. Control Optim., 1987, vol. 25, no 3, pp. 767–780.
  • 36F. 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
  • 37J. C. Doyle, B. A. Francis, A. R. Tannenbaum.

    Feedback control theory, Macmillan Publishing Company, New York, 1992, xii+227 p.
  • 38L. 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/
  • 39A. Figalli, L. Rifford.

    Closing Aubry sets, under preparation.
  • 40A. 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
  • 41A. Figalli, L. Rifford, C. Villani.

    Tangent cut loci on surfaces, in: Differential Geom. Appl., 2011, vol. 29, no 2, pp. 154–159.
  • 42A. Figalli, L. Rifford, C. Villani.

    Nearly round spheres look convex, in: Amer. J. Math., 2012, vol. 134, no 1, pp. 109–139.

    http://dx.doi.org/10.1353/ajm.2012.0000
  • 43M. 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://citeseer.uark.edu:8080/citeseerx/viewdoc/summary?doi=10.1.1.66.8871
  • 44S. 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.
  • 45A. Isidori.

    Nonlinear Control Systems, Comm. in Control Engineering, 3rd, Springer-Verlag, 1995.
  • 46N. Juillet.

    Geometric inequalities and generalized Ricci bounds in the Heisenberg group, in: Int. Math. Res. Not. IMRN, 2009, vol. 13, pp. 2347–2373.
  • 47V. Jurdjevic.

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

    http://dx.doi.org/10.2307/2375037
  • 48T. Kailath.

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  • 49L. 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.

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  • 50W. Klingenberg.

    Lectures on closed geodesics, Grundlehren der Mathematischen Wissenschaften, Springer-Verlag, Berlin, 1978, vol. 230, x+227 p.
  • 51W. Klingenberg, F. Takens.

    Generic properties of geodesic flows, in: Math. Ann., 1972, vol. 197, pp. 323–334.
  • 52E. B. Lee, L. Markus.

    Foundations of optimal control theory, John Wiley & Sons Inc., New York, 1967.
  • 53J. 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
  • 54P. 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
  • 55R. 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
  • 56G. 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
  • 57J.-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
  • 58P. 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
  • 59Q. Mérigot.

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

    http://tel.archives-ouvertes.fr/tel-00443038/
  • 60J.-B. Pomet.

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  • 61L. S. Pontryagin, V. G. Boltjanskiĭ, R. V. Gamkrelidze, E. Mitchenko.

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  • 62L. 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
  • 63L. 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
  • 64L. Rifford.

    Closing Geodesics in C1 Topology, in: J. Differential Geom., 2012, vol. 91, pp. 361-381.

    http://projecteuclid.org/euclid.jdg/1349292669
  • 65L. 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 ]

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  • 66J. A. Sanders, F. Verhulst.

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  • 67K.-T. Sturm.

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

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

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