Bibliography
Publications of the year
Doctoral Dissertations and Habilitation Theses
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1G. Mazanti.
Stability and stabilization of linear switched systems in finite and infinite dimensions, Université Paris-Saclay, École Polytechnique, September 2016.
https://hal.archives-ouvertes.fr/tel-01427215
Articles in International Peer-Reviewed Journals
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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)
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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
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14A. Agrachev, U. Boscain, R. Neel, L. Rizzi.
Intrinsic random walks in Riemannian and sub-Riemannian geometry via volume sampling, January 2016, working paper or preprint.
https://hal.archives-ouvertes.fr/hal-01259762 -
15D. Barilari, U. Boscain, R. W. Neel.
Heat kernel asymptotics on sub-Riemannian manifolds with symmetries and applications to the bi-Heisenberg group, June 2016, working paper or preprint.
https://hal.archives-ouvertes.fr/hal-01327103 -
16Y. Chitour, M. Sigalotti.
Generic controllability of the bilinear Schrödinger equation on 1-D domains: the case of measurable potentials, 2016, working paper or preprint.
https://hal.inria.fr/hal-01292270 -
17N. Juillet, M. Sigalotti.
Pliability, or the whitney extension theorem for curves in carnot groups, 2016, working paper or preprint.
https://hal.inria.fr/hal-01285215 -
18G. Mazanti.
Relative controllability of linear difference equations, April 2016, working paper or preprint.
https://hal.archives-ouvertes.fr/hal-01309166 -
19L. Rizzi, U. Serres.
On the cut locus of free, step two Carnot groups, January 2017, 13 pages. To appear on Proceedings of the AMS.
https://hal.archives-ouvertes.fr/hal-01377408
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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.
http://dx.doi.org/10.1088/1751-8113/41/36/362001 -
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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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88H. J. Sussmann.
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89E. Todorov.
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90G. Turinici.
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91L. Yatsenko, S. Guérin, H. Jauslin.
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92E. Zuazua.
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