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Bibliography

Publications of the year

Doctoral Dissertations and Habilitation Theses

Articles in International Peer-Reviewed Journals

International Conferences with Proceedings

  • 29J. Orłowski, A. Chaillet, M. Sigalotti, A. Destexhe.

    Adaptive scheme for pathological oscillations disruption in a delayed neuronal population model, in: 57th IEEE Conference on Decision and Control, Miami Beach, United States, Proceedings of the 57th IEEE Conference on Decision and Control, December 2018.

    https://hal-centralesupelec.archives-ouvertes.fr/hal-01956472

Conferences without Proceedings

  • 30J.-M. Coron, F. Marbach, F. Sueur, P. Zhang.

    On the controllability of the Navier-Stokes equation in a rectangle, with a little help of a distributed phantom force, in: Journées EDP, Obernai, France, June 2018.

    https://hal.archives-ouvertes.fr/hal-01970878

Scientific Books (or Scientific Book chapters)

Scientific Popularization

Other Publications

References in notes
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    Geometry, analysis and dynamics on sub-Riemannian manifolds. Vol. 1, EMS Series of Lectures in Mathematics, European Mathematical Society (EMS), Zürich, 2016, vi+324 p, Lecture notes from the IHP Trimester held at the Institut Henri Poincaré, Paris and from the CIRM Summer School “Sub-Riemannian Manifolds: From Geodesics to Hypoelliptic Diffusion” held in Luminy, Fall 2014.

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  • 61D. Barilari, U. Boscain, M. Sigalotti (editors)

    Geometry, analysis and dynamics on sub-Riemannian manifolds. Vol. II, EMS Series of Lectures in Mathematics, European Mathematical Society (EMS), Zürich, 2016, viii+299 p, Lecture notes from the IHP Trimester held at the Institut Henri Poincaré, Paris and from the CIRM Summer School “Sub-Riemannian Manifolds: From Geodesics to Hypoelliptic Diffusion” held in Luminy, Fall 2014.

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  • 62R. Adami, U. Boscain.

    Controllability of the Schrödinger Equation via Intersection of Eigenvalues, in: Proceedings of the 44th IEEE Conference on Decision and Control, 2005, pp. 1080–1085.
  • 63A. A. Agrachev.

    Some open problems, in: Geometric control theory and sub-Riemannian geometry, Springer INdAM Ser., Springer, Cham, 2014, vol. 5, pp. 1–13.
  • 64A. Agrachev, D. Barilari, L. Rizzi.

    Curvature: a variational approach, in: Mem. Amer. Math. Soc., 2018, vol. 256, no 1225, v+142 p.
  • 65A. A. Agrachev, Y. Baryshnikov, D. Liberzon.

    On robust Lie-algebraic stability conditions for switched linear systems, in: Systems Control Lett., 2012, vol. 61, no 2, pp. 347–353.

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    The intrinsic hypoelliptic Laplacian and its heat kernel on unimodular Lie groups, in: J. Funct. Anal., 2009, vol. 256, no 8, pp. 2621–2655.

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    Generalized Ricci curvature bounds for three dimensional contact subriemannian manifolds, in: Math. Ann., 2014, vol. 360, no 1-2, pp. 209–253.

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

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    Metric measure spaces with Riemannian Ricci curvature bounded from below, in: Duke Math. J., 2014, vol. 163, no 7, pp. 1405–1490.

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  • 70L. 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.
  • 71M. Balde, U. Boscain, P. Mason.

    A note on stability conditions for planar switched systems, in: Internat. J. Control, 2009, vol. 82, no 10, pp. 1882–1888.

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  • 72F. Baudoin, N. Garofalo.

    Curvature-dimension inequalities and Ricci lower bounds for sub-Riemannian manifolds with transverse symmetries, in: J. Eur. Math. Soc. (JEMS), 2017, vol. 19, no 1, pp. 151–219.

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  • 73F. Baudoin, J. Wang.

    Curvature dimension inequalities and subelliptic heat kernel gradient bounds on contact manifolds, in: Potential Anal., 2014, vol. 40, no 2, pp. 163–193.

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    Analytical parameterization of rotors and proof of a Goldberg conjecture by optimal control theory, in: SIAM J. Control Optim., 2008, vol. 47, no 6, pp. 3007–3036. [ DOI : 10.1137/070705325 ]
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    Controllability of a quantum particle in a moving potential well, in: J. Funct. Anal., 2006, vol. 232, no 2, pp. 328–389.
  • 76M. Benaïm, S. Le Borgne, F. Malrieu, P.-A. Zitt.

    Qualitative properties of certain piecewise deterministic Markov processes, in: Ann. Inst. Henri Poincaré Probab. Stat., 2015, vol. 51, no 3, pp. 1040–1075.

    https://doi.org/10.1214/14-AIHP619
  • 77B. Berret, C. Darlot, F. Jean, T. Pozzo, C. Papaxanthis, J. P. Gauthier.

    The inactivation principle: mathematical solutions minimizing the absolute work and biological implications for the planning of arm movements, in: PLoS Comput. Biol., 2008, vol. 4, no 10, e1000194, 25 p.

    https://doi.org/10.1371/journal.pcbi.1000194
  • 78F. Blanchini.

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

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  • 79F. 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.

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  • 80A. 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.
  • 81M. Born, V. Fock.

    Beweis des adiabatensatzes, in: Zeitschrift für Physik A Hadrons and Nuclei, 1928, vol. 51, no 3–4, pp. 165–180.
  • 82U. Boscain.

    Stability of planar switched systems: the linear single input case, in: SIAM J. Control Optim., 2002, vol. 41, no 1, pp. 89–112. [ DOI : 10.1137/S0363012900382837 ]
  • 83U. Boscain, M. Caponigro, T. Chambrion, M. Sigalotti.

    A weak spectral condition for the controllability of the bilinear Schrödinger equation with application to the control of a rotating planar molecule, in: Comm. Math. Phys., 2012, vol. 311, no 2, pp. 423–455.

    https://doi.org/10.1007/s00220-012-1441-z
  • 84U. Boscain, M. Caponigro, M. Sigalotti.

    Multi-input Schrödinger equation: controllability, tracking, and application to the quantum angular momentum, in: J. Differential Equations, 2014, vol. 256, no 11, pp. 3524–3551.

    https://doi.org/10.1016/j.jde.2014.02.004
  • 85U. Boscain, G. Charlot, M. Sigalotti.

    Stability of planar nonlinear switched systems, in: Discrete Contin. Dyn. Syst., 2006, vol. 15, no 2, pp. 415–432.

    https://doi.org/10.3934/dcds.2006.15.415
  • 86U. Boscain, R. A. Chertovskih, J. P. Gauthier, A. O. Remizov.

    Hypoelliptic diffusion and human vision: a semidiscrete new twist, in: SIAM J. Imaging Sci., 2014, vol. 7, no 2, pp. 669–695. [ DOI : 10.1137/130924731 ]
  • 87U. Boscain, F. Chittaro, P. Mason, M. Sigalotti.

    Adiabatic control of the Schroedinger equation via conical intersections of the eigenvalues, in: IEEE Trans. Automat. Control, 2012, vol. 57, no 8, pp. 1970–1983.
  • 88U. Boscain, J. Duplaix, J.-P. Gauthier, F. Rossi.

    Anthropomorphic image reconstruction via hypoelliptic diffusion, in: SIAM J. Control Optim., 2012, vol. 50, no 3, pp. 1309–1336. [ DOI : 10.1137/11082405X ]
  • 89M. S. Branicky.

    Multiple Lyapunov functions and other analysis tools for switched and hybrid systems, in: IEEE Trans. Automat. Control, 1998, vol. 43, no 4, pp. 475–482, Hybrid control systems.

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  • 90R. W. Brockett.

    System theory on group manifolds and coset spaces, in: SIAM J. Control, 1972, vol. 10, pp. 265–284.
  • 91F. Bullo, A. D. Lewis.

    Geometric control of mechanical systems, Texts in Applied Mathematics, Springer-Verlag, New York, 2005, vol. 49, xxiv+726 p, Modeling, analysis, and design for simple mechanical control systems. [ DOI : 10.1007/978-1-4899-7276-7 ]
  • 92C. Carathéodory.

    Untersuchungen über die Grundlagen der Thermodynamik, in: Math. Ann., 1909, vol. 67, no 3, pp. 355–386.

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  • 93E. Cartan.

    Sur la represéntation géométrique des systèmes matériels non holonomes, in: Proceedings of the International Congress of Mathematicians. Volume 4., 1928, pp. 253–261.
  • 94T. Chambrion, P. Mason, M. Sigalotti, U. Boscain.

    Controllability of the discrete-spectrum Schrödinger equation driven by an external field, in: Ann. Inst. H. Poincaré Anal. Non Linéaire, 2009, vol. 26, no 1, pp. 329–349.

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  • 95G. 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.

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  • 96F. Colonius, G. Mazanti.

    Decay rates for stabilization of linear continuous-time systems with random switching, in: Math. Control Relat. Fields, 2019.
  • 97J.-M. Coron.

    Control and nonlinearity, Mathematical Surveys and Monographs, American Mathematical Society, Providence, RI, 2007, vol. 136, xiv+426 p.
  • 98J.-M. Coron.

    On the controllability of nonlinear partial differential equations, in: Proceedings of the International Congress of Mathematicians. Volume I, Hindustan Book Agency, New Delhi, 2010, pp. 238–264.
  • 99J.-M. Coron.

    Global asymptotic stabilization for controllable systems without drift, in: Math. Control Signals Systems, 1992, vol. 5, no 3, pp. 295–312.

    https://doi.org/10.1007/BF01211563
  • 100D. D'Alessandro.

    Introduction to quantum control and dynamics, Chapman & Hall/CRC Applied Mathematics and Nonlinear Science Series, Chapman & Hall/CRC, Boca Raton, FL, 2008, xiv+343 p.
  • 101W. 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
  • 102R. Duits, E. Franken.

    Left-invariant diffusions on the space of positions and orientations and their application to crossing-preserving smoothing of HARDI images, in: Int. J. Comput. Vis., 2011, vol. 92, no 3, pp. 231–264.

    https://doi.org/10.1007/s11263-010-0332-z
  • 103M. 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.

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  • 104J. Foisy, M. Alfaro, J. Brock, N. Hodges, J. Zimba.

    The standard double soap bubble in 𝐑2 uniquely minimizes perimeter, in: Pacific J. Math., 1993, vol. 159, no 1, pp. 47–59.

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  • 105A. Franci, R. Sepulchre.

    A three-scale model of spatio-temporal bursting, in: SIAM J. Appl. Dyn. Syst., 2016, vol. 15, no 4, pp. 2143–2175. [ DOI : 10.1137/15M1046101 ]
  • 106S. J. Glaser, U. Boscain, T. Calarco, C. P. Koch, W. Köckenberger, R. Kosloff, I. Kuprov, B. Luy, S. Schirmer, T. Schulte-Herbrüggen, D. Sugny, F. K. Wilhelm.

    Training Schrödinger's cat: quantum optimal control. Strategic report on current status, visions and goals for research in Europe, in: European Physical Journal D, 2015, vol. 69, 279 p. [ DOI : 10.1140/epjd/e2015-60464-1 ]
  • 107E. Hakavuori, E. Le Donne.

    Non-minimality of corners in subriemannian geometry, in: Invent. Math., 2016, pp. 1–12. [ DOI : 10.1007/s00222-016-0661-9 ]
  • 108R. K. Hladky, S. D. Pauls.

    Minimal surfaces in the roto-translation group with applications to a neuro-biological image completion model, in: J. Math. Imaging Vision, 2010, vol. 36, no 1, pp. 1–27.

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  • 109D. Hubel, T. Wiesel.

    Brain and Visual Perception: The Story of a 25-Year Collaboration, Oxford University Press, Oxford, 2004.
  • 110V. Jurdjevic.

    Geometric control theory, Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge, 1997, vol. 52, xviii+492 p.
  • 111V. Jurdjevic, H. J. Sussmann.

    Control systems on Lie groups, in: J. Differential Equations, 1972, vol. 12, pp. 313–329.

    https://doi.org/10.1016/0022-0396(72)90035-6
  • 112M. Keyl, R. Zeier, T. Schulte-Herbrueggen.

    Controlling Several Atoms in a Cavity, in: New J. Phys., 2014, vol. 16, 065010 p.
  • 113F. Küsters, S. Trenn.

    Switch observability for switched linear systems, in: Automatica J. IFAC, 2018, vol. 87, pp. 121–127.

    https://doi.org/10.1016/j.automatica.2017.09.024
  • 114E. Le Donne, G. P. Leonardi, R. Monti, D. Vittone.

    Extremal Curves in Nilpotent Lie Groups, in: Geom. Funct. Anal., jul 2013, vol. 23, no 4, pp. 1371–1401. [ DOI : 10.1007/s00039-013-0226-7 ]

    http://arxiv.org/abs/1207.3985
  • 115Z. Leghtas, A. Sarlette, P. Rouchon.

    Adiabatic passage and ensemble control of quantum systems, in: Journal of Physics B, 2011, vol. 44, no 15.
  • 116C. Li, I. Zelenko.

    Jacobi equations and comparison theorems for corank 1 sub-Riemannian structures with symmetries, in: J. Geom. Phys., 2011, vol. 61, no 4, pp. 781–807.

    https://doi.org/10.1016/j.geomphys.2010.12.009
  • 117D. 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.

    https://doi.org/10.1016/S0167-6911(99)00012-2
  • 118D. Liberzon.

    Switching in systems and control, Systems & Control: Foundations & Applications, Birkhäuser Boston, Inc., Boston, MA, 2003, xiv+233 p.

    https://doi.org/10.1007/978-1-4612-0017-8
  • 119D. Liberzon.

    Calculus of variations and optimal control theory, Princeton University Press, Princeton, NJ, 2012, xviii+235 p, A concise introduction.
  • 120H. 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.

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  • 121W. 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. [ DOI : 10.1137/S0363012994268667 ]
  • 122J. 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.

    https://doi.org/10.4007/annals.2009.169.903
  • 123P. Mason, U. Boscain, Y. Chitour.

    Common polynomial Lyapunov functions for linear switched systems, in: SIAM J. Control Optim., 2006, vol. 45, no 1, pp. 226–245 (electronic). [ DOI : 10.1137/040613147 ]
  • 124P. Mason, M. Sigalotti.

    Generic controllability properties for the bilinear Schrödinger equation, in: Comm. Partial Differential Equations, 2010, vol. 35, no 4, pp. 685–706.

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  • 125L. Massoulié.

    Stability of distributed congestion control with heterogeneous feedback delays, in: IEEE Trans. Automat. Control, 2002, vol. 47, no 6, pp. 895–902, Special issue on systems and control methods for communication networks.

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  • 126M. I. Miller, A. Trouvé, L. Younes.

    Geodesic shooting for computational anatomy, in: J. Math. Imaging Vision, 2006, vol. 24, no 2, pp. 209–228.

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  • 127M. Mirrahimi.

    Lyapunov control of a quantum particle in a decaying potential, in: Ann. Inst. H. Poincaré Anal. Non Linéaire, 2009, vol. 26, no 5, pp. 1743–1765.

    https://doi.org/10.1016/j.anihpc.2008.09.006
  • 128A. P. Molchanov, Y. S. Pyatnitskiy.

    Lyapunov functions that specify necessary and sufficient conditions for absolute stability of nonlinear nonstationary control systems, I, II, III, in: Automat. Remote Control, 1986, vol. 47, pp. 344–354, 443–451, 620–630.
  • 129R. 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.
  • 130R. Monti.

    The regularity problem for sub-Riemannian geodesics, in: Geometric control theory and sub-Riemannian geometry, Springer INdAM Ser., Springer, Cham, 2014, vol. 5, pp. 313–332.

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  • 131R. Monti, D. Morbidelli.

    Isoperimetric inequality in the Grushin plane, in: J. Geom. Anal., 2004, vol. 14, no 2, pp. 355–368.

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  • 132R. M. Murray, S. S. Sastry.

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

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  • 133G. Nenciu.

    On the adiabatic theorem of quantum mechanics, in: J. Phys. A, 1980, vol. 13, no 2, pp. L15–L18.

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  • 134V. Nersesyan.

    Growth of Sobolev norms and controllability of the Schrödinger equation, in: Comm. Math. Phys., 2009, vol. 290, no 1, pp. 371–387.
  • 135D. Patino, M. Bâja, P. Riedinger, H. Cormerais, J. Buisson, C. Iung.

    Alternative control methods for DC-DC converters: an application to a four-level three-cell DC-DC converter, in: Internat. J. Robust Nonlinear Control, 2011, vol. 21, no 10, pp. 1112–1133.

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  • 136J. Petitot.

    Neurogéomètrie de la vision. Modèles mathématiques et physiques des architectures fonctionnelles, Les Éditions de l'École Polythechnique, 2008.
  • 137J. Ruess, J. Lygeros.

    Moment-based methods for parameter inference and experiment design for stochastic biochemical reaction networks, in: ACM Trans. Model. Comput. Simul., 2015, vol. 25, no 2, Art. 8, 25 p.

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  • 138A. Sarti, G. Citti, J. Petitot.

    The symplectic structure of the primary visual cortex, in: Biol. Cybernet., 2008, vol. 98, no 1, pp. 33–48.

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  • 139H. Schättler, U. Ledzewicz.

    Geometric optimal control, Interdisciplinary Applied Mathematics, Springer, New York, 2012, vol. 38, xx+640 p, Theory, methods and examples.

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  • 140H. Schättler, U. Ledzewicz.

    Optimal control for mathematical models of cancer therapies, Interdisciplinary Applied Mathematics, Springer, New York, 2015, vol. 42, xix+496 p, An application of geometric methods.

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  • 141R. 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. [ DOI : 10.1137/05063516X ]
  • 142S. Solmaz, R. Shorten, K. Wulff, F. Ó Cairbre.

    A design methodology for switched discrete time linear systems with applications to automotive roll dynamics control, in: Automatica J. IFAC, 2008, vol. 44, no 9, pp. 2358–2363.

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  • 143E. D. Sontag.

    Input to state stability: basic concepts and results, in: Nonlinear and optimal control theory, Lecture Notes in Math., Springer, Berlin, 2008, vol. 1932, pp. 163–220.

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  • 144K.-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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  • 145K.-T. Sturm.

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

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  • 146Z. Sun, S. S. Ge, T. H. Lee.

    Controllability and reachability criteria for switched linear systems, in: Automatica J. IFAC, 2002, vol. 38, no 5, pp. 775–786.

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  • 147Z. Sun, S. S. Ge.

    Stability theory of switched dynamical systems, Communications and Control Engineering Series, Springer, London, 2011, xx+253 p.

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  • 148H. J. Sussmann.

    A regularity theorem for minimizers of real-analytic subriemannian metrics, in: 53rd IEEE Conference on Decision and Control, 2014, pp. 4801-4806.
  • 149K. Tan, X. Yang.

    Subriemannian geodesics of Carnot groups of step 3, in: ESAIM Control Optim. Calc. Var., 2013, vol. 19, no 1, pp. 274–287.

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  • 150S. Teufel.

    Adiabatic perturbation theory in quantum dynamics, Lecture Notes in Mathematics, Springer-Verlag, Berlin, 2003, vol. 1821, vi+236 p.
  • 151A. Trouvé, L. Younes.

    Metamorphoses through Lie group action, in: Found. Comput. Math., 2005, vol. 5, no 2, pp. 173–198.

    https://doi.org/10.1007/s10208-004-0128-z
  • 152E. Trélat.

    Contrôle optimal, Mathématiques Concrètes. [Concrete Mathematics], Vuibert, Paris, 2005, vi+246 p, Théorie & applications. [Theory and applications].
  • 153M. Tucsnak, G. Weiss.

    Observation and control for operator semigroups, Birkhäuser Advanced Texts: Basler Lehrbücher. [Birkhäuser Advanced Texts: Basel Textbooks], Birkhäuser Verlag, Basel, 2009, xii+483 p.

    https://doi.org/10.1007/978-3-7643-8994-9
  • 154G. 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.
  • 155M. Viana.

    Lectures on Lyapunov exponents, Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge, 2014, vol. 145, xiv+202 p.

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  • 156R. Vinter.

    Optimal control, Systems & Control: Foundations & Applications, Birkhäuser Boston, Inc., Boston, MA, 2000, xviii+507 p.
  • 157D. Wisniacki, G. Murgida, P. Tamborenea.

    Quantum control using diabatic and adiabatic transitions, in: AIP Conference Proceedings, AIP, 2007, vol. 963, no 2, pp. 840–842.
  • 158L. Yatsenko, S. Guérin, H. Jauslin.

    Topology of adiabatic passage, in: Phys. Rev. A, 2002, vol. 65, 043407, 7 p.
  • 159A. van der Schaft, H. Schumacher.

    An introduction to hybrid dynamical systems, Lecture Notes in Control and Information Sciences, Springer-Verlag London, Ltd., London, 2000, vol. 251, xiv+174 p.

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