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Bibliography

Publications of the year

Doctoral Dissertations and Habilitation Theses

  • 1A. Hindawi.

    Transport Optimal en Théorie du Contrôle, Univ. de Nice - Sophia Antipolis, June 2012.

Articles in International Peer-Reviewed Journals

  • 2A. Bombrun, J.-B. Pomet.

    The averaged control system of fast oscillating control systems, in: SIAM J. Control Optim., 2013, to appear.

    http://hal.inria.fr/hal-00648330/
  • 3B. Bonnard, J.-B. Caillau, G. Janin.

    Conjugate-cut loci and injectivity domains on two-spheres of revolution, in: ESAIM Control Optim. Calc. Var., 2013, to appear.

    http://www.esaim-cocv.org/
  • 4B. Bonnard, M. Chyba, J. Marriott.

    A Geometric Question in the Contrast Imaging Problem in Nuclear Magnetic Resonance, in: Math. Control Relat. Fields, 2013, to appear (special issue “Geometric Optimal Control”).
  • 5B. Bonnard, M. Chyba, J. Marriott.

    Singular Trajectories and the Contrast Imaging Problem in Nuclear Magnetic Resonance, in: SIAM J. Control Optim., 2013, to appear.
  • 6B. Bonnard, O. Cots.

    Geometric Numerical Methods and Results in the Control Imaging Problem in Nuclear Magnetic Resonance, in: Math. Models Methods Appl. Sci., 2013, to appear.

    http://www.worldscientific.com/worldscinet/m3as
  • 7B. 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, p. 1957-1969. [ DOI : 10.1109/TAC.2012.2195859 ]

    http://hal.archives-ouvertes.fr/hal-00750032/
  • 8B. Bonnard, O. Cots, N. Shcherbakova.

    The Serret-Andoyer Riemannian metric and Euler-Poinsot rigid body motion, in: Math. Control Relat. Fields, 2013, to appear (special issue “Geometric Optimal Control”).
  • 9B. Bonnard, S. J. Glaser, D. Sugny.

    A review of geometric optimal control for quantum systems in nuclear magnetic resonance, in: Adv. Math. Phys., 2012, Art. ID 857493, 29 p. [ DOI : 10.1155/2012/857493 ]

    http://hal.archives-ouvertes.fr/hal-00750040/
  • 10A. Figalli, L. Rifford, C. Villani.

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

    http://dx.doi.org/10.1353/ajm.2012.0000
  • 11L. Rifford.

    Closing Geodesics in C 1 Topology, in: J. Differential Geom., 2012, vol. 91, p. 361-381.

    http://projecteuclid.org/euclid.jdg/1349292669
  • 12L. Rifford.

    Ricci curvatures in Carnot groups, in: Math. Control Relat. Fields, 2013, to appear (special issue “Geometric Optimal Control”).
  • 13L. 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

International Conferences with Proceedings

  • 14B. Bonnard, M. Chyba, J. Marriott, G. Picot.

    Singular trajectories in the contrast problem in nuclear magnetic resonance, in: 5th Internat. Conf. on Optimization and Control with Application, Beijing, December 2012.
  • 15B. Bonnard, O. Cots, L. Jassionnesse.

    Geometric and numerical techniques to compute conjugate and cut loci on Riemannian surfaces, in: INDAM meeting on Geometric Control and sub-Riemannian Geometry, May 2012, Proceedings to appear in 2013.

    http://www.cmap.polytechnique.fr/geometric-control-srg/
  • 16L. Rifford.

    Sub-Riemannian Geometry and Optimal Transport, in: Géométrie sous-riemannienne, CIMPA school in Beyrouth, Lebanon, February 2012, CIMPA, 2013, lecture notes to appear.

Conferences without Proceedings

  • 17L. Rifford.

    From the Poincaré “lignes de partage” to the convex earth theorem, in: International Conference “Henri Poincaré : du mathématicien au philosophe”, Paris, Institut Henri Poincaré, November 2012.

Scientific Books (or Scientific Book chapters)

  • 18B. 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.

Other Publications

  • 19B. Bonnard, J.-B. Caillau.

    Metrics with equatorial singularities on the sphère, 2012, submitted to Annali di Matematica Pura ed Applicata.

    http://www.sciencedirect.com/science/journal/09262245
  • 20B. Bonnard, O. Cots, N. Shcherbakova.

    Riemannian metrics on 2d-manifolds related to the Euler-Poinsot rigid body motion, 2012, submitted to Ann. Inst. H. Poincaré Anal. Non Linéaire.
  • 21A. Figalli, L. Rifford.

    Closing Aubry sets I & II, 2012, submitted.
References in notes
  • 22A. Agrachev, P. Lee.

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

    http://dx.doi.org/10.1090/S0002-9947-09-04813-2
  • 23A. Agrachev, P. 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
  • 24A. 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.
  • 25L. Ambrosio, S. Rigot.

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

    http://dx.doi.org/10.1016/S0022-1236(03)00019-3
  • 26V. I. Arnold.

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  • 27Z. Artstein.

    Stabilization with relaxed control, in: Nonlinear Analysis TMA, November 1983, vol. 7, no 11, p. 1163-1173.
  • 28E. Belbruno.

    Capture dynamics and chaotic motions in celestial mechanics, Princeton University Press, Princeton, NJ, 2004, xx+211 p.
  • 29A. Bombrun, J. Chetboun, J.-B. Pomet.

    Transferts Terre-Lune en poussée faible par contrôle feedback. La mission Smart-1, Inria, July 2006, no 5955.

    http://hal.inria.fr/inria-00087927
  • 30B. 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, p. 395–411.
  • 31B. Bonnard, J.-B. Caillau.

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

    http://dx.doi.org/10.1515/FORUM.2009.038
  • 32B. Bonnard, J.-B. Caillau, G. Picot.

    Geometric and numerical techniques in optimal control of two and three-body problems, in: Commun. Inf. Syst., 2010, vol. 10, no 4, p. 239–278.

    http://projecteuclid.org/getRecord?id=euclid.cis/1290608950
  • 33B. 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, p. 1315–1318.

    http://dx.doi.org/10.1016/j.crma.2010.10.036
  • 34B. Bonnard, M. Chyba.

    Singular trajectories and their role in control theory, Mathématiques & Applications, Springer-Verlag, Berlin, 2003, vol. 40, xvi+357 p.
  • 35B. 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, p. 267–292.

    http://dx.doi.org/10.1051/cocv/2010004
  • 36B. 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, p. 1289–1308.

    http://dx.doi.org/10.1137/080717043
  • 37U. 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.
  • 38Y. Brenier.

    Décomposition polaire et ré-arrangement monotone des champs de vecteurs, in: C. R. Acad. Sci. Paris Sér. I Math., 1987, vol. 305, p. 805-808.
  • 39Y. Brenier.

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

    http://dx.doi.org/10.1002/cpa.3160440402
  • 40F. Chaplais.

    Averaging and deterministic optimal control, in: SIAM J. Control Optim., 1987, vol. 25, no 3, p. 767–780.
  • 41F. 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, p. 25–48 (electronic).

    http://dx.doi.org/10.1137/S0363012999352297
  • 42J. C. Doyle, B. A. Francis, A. R. Tannenbaum.

    Feedback control theory, Macmillan Publishing Company, New York, 1992, xii+227 p.
  • 43L. Faubourg, J.-B. Pomet.

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

    http://www.edpsciences.org/cocv/
  • 44L. Faubourg, J.-B. Pomet.

    Nonsmooth functions and uniform limits of control Lyapunov functions, in: 41st IEEE Conf. on Decision and Control, Las Vegas (USA), December 2002.
  • 45A. Figalli, L. Rifford.

    Closing Aubry sets, under preparation.
  • 46A. Figalli, L. Rifford.

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

    http://dx.doi.org/10.1007/s00039-010-0053-z
  • 47A. Figalli, L. Rifford, C. Villani.

    Tangent cut loci on surfaces, in: Differential Geom. Appl., 2011, vol. 29, no 2, p. 154–159.
  • 48M. 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, p. 1327-1361.

    http://dx.doi.org/10.1080/00207179508921959
  • 49S. 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.
  • 50A. Hindawi, J.-B. Pomet, L. Rifford.

    Mass transportation with LQ cost functions, in: Acta Appl. Math., 2011, vol. 113, no 2, p. 215–229. [ DOI : 10.1007/s10440-010-9595-1 ]

    http://hal.archives-ouvertes.fr/hal-00534083/
  • 51A. Isidori.

    Nonlinear Control Systems, Comm. in Control Engineering, 3rd, Springer-Verlag, 1995.
  • 52Z.-P. Jiang, I. M. Mareels, J.-B. Pomet.

    Output Feedback Global Stabilization for a Class of Nonlinear Systems with Unmodeled Dynamics, in: Europ. J. Control, 1996, vol. 2, p. 201-210.
  • 53Z.-P. Jiang, J.-B. Pomet.

    Global Stabilization of Parametric Chained-form Systems by Time-varying Dynamic Feedback, in: Int. J. of Adaptive Control and Signal Processing, 1996, vol. 10, p. 47-59.
  • 54N. Juillet.

    Geometric inequalities and generalized Ricci bounds in the Heisenberg group, in: Int. Math. Res. Not. IMRN, 2009, vol. 13, p. 2347–2373.
  • 55V. Jurdjevic.

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

    http://dx.doi.org/10.2307/2375037
  • 56T. Kailath.

    Linear systems, Information and System Sciences, Prentice-Hall Inc., Englewood Cliffs, N.J., 1980.
  • 57L. V. Kantorovich.

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

    http://dx.doi.org/10.1007/s10958-006-0050-9
  • 58W. Klingenberg.

    Lectures on closed geodesics, Springer-Verlag, Berlin, 1978, x+227 p, Grundlehren der Mathematischen Wissenschaften, Vol. 230.
  • 59W. Klingenberg, F. Takens.

    Generic properties of geodesic flows, in: Math. Ann., 1972, vol. 197, p. 323–334.
  • 60E. B. Lee, L. Markus.

    Foundations of optimal control theory, John Wiley & Sons Inc., New York, 1967.
  • 61J. Lott, C. Villani.

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

    http://dx.doi.org/10.4007/annals.2009.169.903
  • 62J. E. Marsden, S. D. Ross.

    New methods in celestial mechanics and mission design, in: Bull. Amer. Math. Soc. (N.S.), 2006, vol. 43, no 1, p. 43–73 (electronic).

    http://dx.doi.org/10.1090/S0273-0979-05-01085-2
  • 63P. 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, p. 705–768 (electronic).

    http://users.ictp.it/~pub_off/lectures/lns008/Rouchon/Rouchon.pdf
  • 64R. J. McCann.

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

    http://dx.doi.org/10.1007/PL00001679
  • 65G. Monge.

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

    http://gallica.bnf.fr/ark:/12148/bpt6k35800.image.f796
  • 66J.-M. Morel, F. Santambrogio.

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

    http://dx.doi.org/10.1016/j.aml.2006.05.009
  • 67P. 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, p. 22-49.

    http://dx.doi.org/10.1137/S0363012997315427
  • 68P. Morin, C. Samson, J.-B. Pomet, Z.-P. Jiang.

    Time-varying Feedback Stabilization of the Attitude of a Rigid Spacecraft with two controls, in: Syst. & Control Lett., 1995, vol. 25, p. 375-385.
  • 69Q. Mérigot.

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

    http://tel.archives-ouvertes.fr/tel-00443038/
  • 70J.-B. Pomet, R. M. Hirshorn, W. A. Cebuhar.

    Dynamic Output Feedback Regulation for a class of nonlinear systems, in: Math. of Control, Signals and Systems, 1993, vol. 6, no 2, p. 106-124.
  • 71J.-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, p. 147-158.
  • 72L. S. Pontryagin, V. G. Boltjanskiĭ, R. V. Gamkrelidze, E. Mitchenko.

    Théorie mathématique des processus optimaux, Editions MIR, Moscou, 1974.
  • 73G. e. a. Racca.

    SMART-1 mission descriptioin and development status, in: Planetary and space science, 2002, vol. 50, p. 1323-1337.
  • 74L. Rifford.

    Existence of Lipschitz and semiconcave control-Lyapunov functions, in: SIAM J. Control Optim., 2000, vol. 39, no 4, p. 1043–1064 (electronic).

    http://dx.doi.org/10.1137/S0363012999356039
  • 75L. Rifford.

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

    http://dx.doi.org/10.1051/cocv:2001124
  • 76L. Rifford.

    Range of the gradient of a smooth bump function in finite dimensions, in: Proc. Amer. Math. Soc., 2003, vol. 131, no 10, p. 3063–3066 (electronic).

    http://dx.doi.org/10.1090/S0002-9939-03-07078-3
  • 77L. Rifford.

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

    http://dx.doi.org/10.1016/j.jde.2005.10.017
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  • 79K.-T. Sturm.

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

    http://dx.doi.org/10.1007/s11511-006-0002-8
  • 80K.-T. Sturm.

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

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


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