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Bibliography

Publications of the year

Doctoral Dissertations and Habilitation Theses

Articles in International Peer-Reviewed Journals

  • 2A. Agrachev, D. Barilari, L. Rizzi.

    Sub-Riemannian curvature in contact geometry, in: Journal of Geometric Analysis, 2016. [ DOI : 10.1007/s12220-016-9684-0 ]

    https://hal.archives-ouvertes.fr/hal-01160901
  • 3D. Barilari, U. Boscain, G. Charlot, R. W. Neel.

    On the heat diffusion for generic Riemannian and sub-Riemannian structures, in: International Mathematics Research Notices, 2016, vol. 2016, pp. 1-34, 26 pages, 1 figure.

    https://hal.archives-ouvertes.fr/hal-00879444
  • 4A. Bohi, D. Prandi, V. Guis, F. Bouchara, J.-P. Gauthier.

    Fourier Descriptors Based on the Structure of the Human Primary Visual Cortex with Applications to Object Recognition, in: Journal of Mathematical Imaging and Vision, July 2016, pp. 1-17. [ DOI : 10.1007/s10851-016-0669-1 ]

    https://hal.archives-ouvertes.fr/hal-01383846
  • 5U. Boscain, D. Prandi.

    Self-adjoint extensions and stochastic completeness of the Laplace–Beltrami operator on conic and anticonic surfaces, in: Journal of Differential Equations, February 2016, vol. 260, no 4, pp. 3234–3269, 28 pages, 2 figures. [ DOI : 10.1016/j.jde.2015.10.011 ]

    https://hal.archives-ouvertes.fr/hal-00848792
  • 6U. Boscain, D. Prandi, M. Seri.

    Spectral analysis and the Aharonov-Bohm effect on certain almost-Riemannian manifolds, in: Communications in Partial Differential Equations, 2016, vol. 41, no 1, pp. 32–50, 28 pages, 6 figures. [ DOI : 10.1080/03605302.2015.1095766 ]

    https://hal.archives-ouvertes.fr/hal-01019955
  • 7U. Boscain, L. Sacchelli, M. Sigalotti.

    Generic singularities of line fields on 2D manifolds, in: Differential Geometry and its Applications, September 2016, vol. Volume 49, no December 2016, pp. 326–350.

    https://hal.archives-ouvertes.fr/hal-01318515
  • 8Y. Chitour, G. Mazanti, M. Sigalotti.

    Persistently damped transport on a network of circles, in: Transactions of the American Mathematical Society, October 2016. [ DOI : 10.1090/tran/6778 ]

    https://hal.inria.fr/hal-00999743
  • 9Y. Chitour, G. Mazanti, M. Sigalotti.

    Stability of non-autonomous difference equations with applications to transport and wave propagation on networks, in: Networks and Heterogeneous Media, December 2016, vol. 11, pp. 563-601. [ DOI : 10.3934/nhm.2016010 ]

    https://hal.archives-ouvertes.fr/hal-01139814
  • 10L. Rizzi.

    Measure contraction properties of Carnot groups, in: Calculus of Variations and Partial Differential Equations, May 2016. [ DOI : 10.1007/s00526-016-1002-y ]

    https://hal.archives-ouvertes.fr/hal-01218376

Scientific Books (or Scientific Book chapters)

  • 11A. Agrachev, D. Barilari, U. Boscain.

    Introduction to geodesics in sub-Riemannian geometry, in: Geometry, Analysis and Dynamics on Sub-Riemannian Manifolds - Volume II, EMS Series of Lectures in Mathematics, 2016.

    https://hal.inria.fr/hal-01392516
  • 12D. Barilari, U. Boscain, M. Sigalotti.

    Geometry, Analysis and Dynamics on sub-Riemannian Manifolds - Volume I, EMS Series of Lectures in Mathematics, European Mathematical Society, 2016. [ DOI : 10.4171/162 ]

    https://hal.archives-ouvertes.fr/hal-01390381
  • 13D. Barilari, U. Boscain, M. Sigalotti.

    Geometry, Analysis and Dynamics on sub-Riemannian Manifolds - Volume II, EMS Series of Lectures in Mathematics, European Mathematical Society, 2016. [ DOI : 10.4171/163 ]

    https://hal.archives-ouvertes.fr/hal-01390382

Other Publications

References in notes
  • 20A. A. Agrachev, T. Chambrion.

    An estimation of the controllability time for single-input systems on compact Lie groups, in: ESAIM Control Optim. Calc. Var., 2006, vol. 12, no 3, pp. 409–441.
  • 21A. A. Agrachev, D. Liberzon.

    Lie-algebraic stability criteria for switched systems, in: SIAM J. Control Optim., 2001, vol. 40, no 1, pp. 253–269.

    http://dx.doi.org/10.1137/S0363012999365704
  • 22A. A. 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.
  • 23A. A. Agrachev, A. V. Sarychev.

    Navier-Stokes equations: controllability by means of low modes forcing, in: J. Math. Fluid Mech., 2005, vol. 7, no 1, pp. 108–152.

    http://dx.doi.org/10.1007/s00021-004-0110-1
  • 24F. Albertini, D. D'Alessandro.

    Notions of controllability for bilinear multilevel quantum systems, in: IEEE Trans. Automat. Control, 2003, vol. 48, no 8, pp. 1399–1403.
  • 25C. Altafini.

    Controllability properties for finite dimensional quantum Markovian master equations, in: J. Math. Phys., 2003, vol. 44, no 6, pp. 2357–2372.
  • 26L. Ambrosio, P. Tilli.

    Topics on analysis in metric spaces, Oxford Lecture Series in Mathematics and its Applications, Oxford University Press, Oxford, 2004, vol. 25, viii+133 p.
  • 27G. Arechavaleta, J.-P. Laumond, H. Hicheur, A. Berthoz.

    An optimality principle governing human locomotion, in: IEEE Trans. on Robotics, 2008, vol. 24, no 1.
  • 28L. Baudouin.

    A bilinear optimal control problem applied to a time dependent Hartree-Fock equation coupled with classical nuclear dynamics, in: Port. Math. (N.S.), 2006, vol. 63, no 3, pp. 293–325.
  • 29L. Baudouin, O. Kavian, J.-P. Puel.

    Regularity for a Schrödinger equation with singular potentials and application to bilinear optimal control, in: J. Differential Equations, 2005, vol. 216, no 1, pp. 188–222.
  • 30L. Baudouin, J. Salomon.

    Constructive solution of a bilinear optimal control problem for a Schrödinger equation, in: Systems Control Lett., 2008, vol. 57, no 6, pp. 453–464.

    http://dx.doi.org/10.1016/j.sysconle.2007.11.002
  • 31K. Beauchard.

    Local controllability of a 1-D Schrödinger equation, in: J. Math. Pures Appl. (9), 2005, vol. 84, no 7, pp. 851–956.
  • 32K. Beauchard, J.-M. Coron.

    Controllability of a quantum particle in a moving potential well, in: J. Funct. Anal., 2006, vol. 232, no 2, pp. 328–389.
  • 33M. Belhadj, J. Salomon, G. Turinici.

    A stable toolkit method in quantum control, in: J. Phys. A, 2008, vol. 41, no 36, 362001, 10 p.

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  • 34F. Blanchini.

    Nonquadratic Lyapunov functions for robust control, in: Automatica J. IFAC, 1995, vol. 31, no 3, pp. 451–461.

    http://dx.doi.org/10.1016/0005-1098(94)00133-4
  • 35F. Blanchini, S. Miani.

    A new class of universal Lyapunov functions for the control of uncertain linear systems, in: IEEE Trans. Automat. Control, 1999, vol. 44, no 3, pp. 641–647.

    http://dx.doi.org/10.1109/9.751368
  • 36A. M. Bloch, R. W. Brockett, C. Rangan.

    Finite Controllability of Infinite-Dimensional Quantum Systems, in: IEEE Trans. Automat. Control, 2010.
  • 37V. D. Blondel, J. Theys, A. A. Vladimirov.

    An elementary counterexample to the finiteness conjecture, in: SIAM J. Matrix Anal. Appl., 2003, vol. 24, no 4, pp. 963–970.

    http://dx.doi.org/10.1137/S0895479801397846
  • 38A. Bonfiglioli, E. Lanconelli, F. Uguzzoni.

    Stratified Lie groups and potential theory for their sub-Laplacians, Springer Monographs in Mathematics, Springer, Berlin, 2007, xxvi+800 p.
  • 39B. 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
  • 40A. Borzì, E. Decker.

    Analysis of a leap-frog pseudospectral scheme for the Schrödinger equation, in: J. Comput. Appl. Math., 2006, vol. 193, no 1, pp. 65–88.
  • 41A. Borzì, U. Hohenester.

    Multigrid optimization schemes for solving Bose-Einstein condensate control problems, in: SIAM J. Sci. Comput., 2008, vol. 30, no 1, pp. 441–462.

    http://dx.doi.org/10.1137/070686135
  • 42C. Brif, R. Chakrabarti, H. Rabitz.

    Control of quantum phenomena: Past, present, and future, Advances in Chemical Physics, S. A. Rice (ed), Wiley, New York, 2010.
  • 43F. Bullo, A. D. Lewis.

    Geometric control of mechanical systems, Texts in Applied Mathematics, Springer-Verlag, New York, 2005, vol. 49, xxiv+726 p.
  • 44R. Cabrera, H. Rabitz.

    The landscape of quantum transitions driven by single-qubit unitary transformations with implications for entanglement, in: J. Phys. A, 2009, vol. 42, no 27, 275303, 9 p.

    http://dx.doi.org/10.1088/1751-8113/42/27/275303
  • 45G. Citti, A. Sarti.

    A cortical based model of perceptual completion in the roto-translation space, in: J. Math. Imaging Vision, 2006, vol. 24, no 3, pp. 307–326.

    http://dx.doi.org/10.1007/s10851-005-3630-2
  • 46J.-M. Coron.

    Control and nonlinearity, Mathematical Surveys and Monographs, American Mathematical Society, Providence, RI, 2007, vol. 136, xiv+426 p.
  • 47W. P. Dayawansa, C. F. Martin.

    A converse Lyapunov theorem for a class of dynamical systems which undergo switching, in: IEEE Trans. Automat. Control, 1999, vol. 44, no 4, pp. 751–760.

    http://dx.doi.org/10.1109/9.754812
  • 48L. El Ghaoui, S.-I. Niculescu.

    Robust decision problems in engineering: a linear matrix inequality approach, in: Advances in linear matrix inequality methods in control, Philadelphia, PA, Adv. Des. Control, SIAM, 2000, vol. 2, pp. 3–37.
  • 49S. Ervedoza, J.-P. Puel.

    Approximate controllability for a system of Schrödinger equations modeling a single trapped ion, in: Ann. Inst. H. Poincaré Anal. Non Linéaire, 2009, vol. 26, pp. 2111–2136.
  • 50M. Fliess, J. Lévine, P. Martin, P. Rouchon.

    Flatness and defect of non-linear systems: introductory theory and examples, in: Internat. J. Control, 1995, vol. 61, no 6, pp. 1327–1361.

    http://dx.doi.org/10.1080/00207179508921959
  • 51B. Franchi, R. Serapioni, F. Serra Cassano.

    Regular hypersurfaces, intrinsic perimeter and implicit function theorem in Carnot groups, in: Comm. Anal. Geom., 2003, vol. 11, no 5, pp. 909–944.
  • 52M. Gugat.

    Optimal switching boundary control of a string to rest in finite time, in: ZAMM Z. Angew. Math. Mech., 2008, vol. 88, no 4, pp. 283–305.
  • 53J. Hespanha, S. Morse.

    Stability of switched systems with average dwell-time, in: Proceedings of the 38th IEEE Conference on Decision and Control, CDC 1999, Phoenix, AZ, USA, 1999, pp. 2655–2660.
  • 54D. Hubel, T. Wiesel.

    Brain and Visual Perception: The Story of a 25-Year Collaboration, Oxford University Press, Oxford, 2004.
  • 55R. Illner, H. Lange, H. Teismann.

    Limitations on the control of Schrödinger equations, in: ESAIM Control Optim. Calc. Var., 2006, vol. 12, no 4, pp. 615–635.

    http://dx.doi.org/10.1051/cocv:2006014
  • 56A. Isidori.

    Nonlinear control systems, Communications and Control Engineering Series, Second, Springer-Verlag, Berlin, 1989, xii+479 p, An introduction.
  • 57K. Ito, K. Kunisch.

    Optimal bilinear control of an abstract Schrödinger equation, in: SIAM J. Control Optim., 2007, vol. 46, no 1, pp. 274–287.
  • 58K. Ito, K. Kunisch.

    Asymptotic properties of feedback solutions for a class of quantum control problems, in: SIAM J. Control Optim., 2009, vol. 48, no 4, pp. 2323–2343.

    http://dx.doi.org/10.1137/080720784
  • 59R. Kalman.

    When is a linear control system optimal?, in: ASME Transactions, Journal of Basic Engineering, 1964, vol. 86, pp. 51–60.
  • 60N. Khaneja, S. J. Glaser, R. W. Brockett.

    Sub-Riemannian geometry and time optimal control of three spin systems: quantum gates and coherence transfer, in: Phys. Rev. A (3), 2002, vol. 65, no 3, part A, 032301, 11 p.
  • 61N. Khaneja, B. Luy, S. J. Glaser.

    Boundary of quantum evolution under decoherence, in: Proc. Natl. Acad. Sci. USA, 2003, vol. 100, no 23, pp. 13162–13166.

    http://dx.doi.org/10.1073/pnas.2134111100
  • 62V. S. Kozyakin.

    Algebraic unsolvability of a problem on the absolute stability of desynchronized systems, in: Avtomat. i Telemekh., 1990, pp. 41–47.
  • 63G. Lafferriere, H. J. Sussmann.

    A differential geometry approach to motion planning, in: Nonholonomic Motion Planning (Z. Li and J. F. Canny, editors), Kluwer Academic Publishers, 1993, pp. 235-270.
  • 64J.-S. Li, N. Khaneja.

    Ensemble control of Bloch equations, in: IEEE Trans. Automat. Control, 2009, vol. 54, no 3, pp. 528–536.

    http://dx.doi.org/10.1109/TAC.2009.2012983
  • 65D. Liberzon, J. P. Hespanha, A. S. Morse.

    Stability of switched systems: a Lie-algebraic condition, in: Systems Control Lett., 1999, vol. 37, no 3, pp. 117–122.

    http://dx.doi.org/10.1016/S0167-6911(99)00012-2
  • 66D. Liberzon.

    Switching in systems and control, Systems & Control: Foundations & Applications, Birkhäuser Boston Inc., Boston, MA, 2003, xiv+233 p.
  • 67H. Lin, P. J. Antsaklis.

    Stability and stabilizability of switched linear systems: a survey of recent results, in: IEEE Trans. Automat. Control, 2009, vol. 54, no 2, pp. 308–322.

    http://dx.doi.org/10.1109/TAC.2008.2012009
  • 68Y. Lin, E. D. Sontag, Y. Wang.

    A smooth converse Lyapunov theorem for robust stability, in: SIAM J. Control Optim., 1996, vol. 34, no 1, pp. 124–160.

    http://dx.doi.org/10.1137/S0363012993259981
  • 69W. Liu.

    Averaging theorems for highly oscillatory differential equations and iterated Lie brackets, in: SIAM J. Control Optim., 1997, vol. 35, no 6, pp. 1989–2020.

    http://dx.doi.org/10.1137/S0363012994268667
  • 70Y. Maday, J. Salomon, G. Turinici.

    Monotonic parareal control for quantum systems, in: SIAM J. Numer. Anal., 2007, vol. 45, no 6, pp. 2468–2482.

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  • 71A. N. Michel, Y. Sun, A. P. Molchanov.

    Stability analysis of discountinuous dynamical systems determined by semigroups, in: IEEE Trans. Automat. Control, 2005, vol. 50, no 9, pp. 1277–1290.

    http://dx.doi.org/10.1109/TAC.2005.854582
  • 72M. Mirrahimi.

    Lyapunov control of a particle in a finite quantum potential well, in: Proceedings of the 45th IEEE Conference on Decision and Control, 2006.
  • 73M. Mirrahimi, P. Rouchon.

    Controllability of quantum harmonic oscillators, in: IEEE Trans. Automat. Control, 2004, vol. 49, no 5, pp. 745–747.
  • 74A. P. Molchanov, Y. S. Pyatnitskiy.

    Criteria of asymptotic stability of differential and difference inclusions encountered in control theory, in: Systems Control Lett., 1989, vol. 13, no 1, pp. 59–64.

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  • 75R. Montgomery.

    A tour of subriemannian geometries, their geodesics and applications, Mathematical Surveys and Monographs, American Mathematical Society, Providence, RI, 2002, vol. 91, xx+259 p.
  • 76R. M. Murray, S. S. Sastry.

    Nonholonomic motion planning: steering using sinusoids, in: IEEE Trans. Automat. Control, 1993, vol. 38, no 5, pp. 700–716.

    http://dx.doi.org/10.1109/9.277235
  • 77V. Nersesyan.

    Growth of Sobolev norms and controllability of the Schrödinger equation, in: Comm. Math. Phys., 2009, vol. 290, no 1, pp. 371–387.
  • 78A. Y. Ng, S. Russell.

    Algorithms for Inverse Reinforcement Learning, in: Proc. 17th International Conf. on Machine Learning, 2000, pp. 663–670.
  • 79J. Petitot.

    Neurogéomètrie de la vision. Modèles mathématiques et physiques des architectures fonctionnelles, Les Éditions de l'École Polythechnique, 2008.
  • 80J. Petitot, Y. Tondut.

    Vers une neurogéométrie. Fibrations corticales, structures de contact et contours subjectifs modaux, in: Math. Inform. Sci. Humaines, 1999, no 145, pp. 5–101.
  • 81H. Rabitz, H. de Vivie-Riedle, R. Motzkus, K. Kompa.

    Wither the future of controlling quantum phenomena?, in: SCIENCE, 2000, vol. 288, pp. 824–828.
  • 82D. Rossini, T. Calarco, V. Giovannetti, S. Montangero, R. Fazio.

    Decoherence by engineered quantum baths, in: J. Phys. A, 2007, vol. 40, no 28, pp. 8033–8040.

    http://dx.doi.org/10.1088/1751-8113/40/28/S12
  • 83P. Rouchon.

    Control of a quantum particle in a moving potential well, in: Lagrangian and Hamiltonian methods for nonlinear control 2003, Laxenburg, IFAC, 2003, pp. 287–290.
  • 84A. Sasane.

    Stability of switching infinite-dimensional systems, in: Automatica J. IFAC, 2005, vol. 41, no 1, pp. 75–78.

    http://dx.doi.org/10.1016/j.automatica.2004.07.013
  • 85A. Saurabh, M. H. Falk, M. B. Alexandre.

    Stability analysis of linear hyperbolic systems with switching parameters and boundary conditions, in: Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008, December 9-11, 2008, Cancún, Mexico, 2008, pp. 2081–2086.
  • 86M. Shapiro, P. Brumer.

    Principles of the Quantum Control of Molecular Processes, Principles of the Quantum Control of Molecular Processes, pp. 250. Wiley-VCH, February 2003.
  • 87R. Shorten, F. Wirth, O. Mason, K. Wulff, C. King.

    Stability criteria for switched and hybrid systems, in: SIAM Rev., 2007, vol. 49, no 4, pp. 545–592.

    http://dx.doi.org/10.1137/05063516X
  • 88H. J. Sussmann.

    A continuation method for nonholonomic path finding, in: Proceedings of the 32th IEEE Conference on Decision and Control, CDC 1993, Piscataway, NJ, USA, 1993, pp. 2718–2723.
  • 89E. Todorov.

    12, in: Optimal control theory, Bayesian Brain: Probabilistic Approaches to Neural Coding, Doya K (ed), 2006, pp. 269–298.
  • 90G. Turinici.

    On the controllability of bilinear quantum systems, in: Mathematical models and methods for ab initio Quantum Chemistry, M. Defranceschi, C. Le Bris (editors), Lecture Notes in Chemistry, Springer, 2000, vol. 74.
  • 91L. Yatsenko, S. Guérin, H. Jauslin.

    Topology of adiabatic passage, in: Phys. Rev. A, 2002, vol. 65, 043407, 7 p.
  • 92E. Zuazua.

    Switching controls, in: Journal of the European Mathematical Society, 2011, vol. 13, no 1, pp. 85–117.


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