Bibliography

Publications of the year

Articles in International Peer-Reviewed Journals

1A. A. Agrachev, D. Barilari, U. Boscain.

On the Hausdorff volume in sub-Riemannian geometry, in: Calculus of Variations and Partial Differential Equations, 2012, vol. 43, n^o 3-4, p. 355–388.

http://dx.doi.org/10.1007/s00526-011-0414-y
2A. Ajami, J.-P. Gauthier, T. Maillot, U. Serres.

How humans fly, in: ESAIM: Control, Optimisation and Calculus of Variations, 2013.
3D. Barilari, U. Boscain, J.-P. Gauthier.

On 2-step, corank 2, nilpotent sub-Riemannian metrics, in: SIAM J. Control Optim., 2012, vol. 50, n^o 1, p. 559–582.

http://dx.doi.org/10.1137/110835700
4D. Barilari, L. Rizzi.

A formula for Popp's volume in sub-Riemannian geometry, in: Analysis and Geometry in Metric Spaces, 2013.

http://arxiv.org/pdf/1211.2325v1.pdf
5N. Boizot, J.-P. Gauthier.

Motion Planning for Kinematic Systems, in: IEEE Transaction on Automatic Control, 2013.
6N. Boizot, J.-P. Gauthier.

On the motion planning of the ball with a trailer, in: Math. control and related fields, 2013.
7U. 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, n^o 2, p. 423–455.

http://dx.doi.org/10.1007/s00220-012-1441-z
8U. Boscain, F. Chittaro, P. Mason, M. Sigalotti.

Adiabatic control of the Schrödinger equation via conical intersections of the eigenvalues, in: IEEE Trans. Automat. Control, 2012, vol. 57, p. 1970–1983.
9U. Boscain, C. Laurent.

The Laplace–Beltrami operator in almost-Riemannian geometry, in: Ann. Inst. Fourier, 2013.
10Y. Chitour, F. Jean, R. Long.

A global steering method for nonholonomic systems, in: Journal of Differential Equations, 2013.

http://dx.doi.org/10.1016/j.jde.2012.11.012
11Y. Chitour, F. Jean, P. Mason.

Optimal control models of goal-oriented human locomotion, in: SIAM J. Control Optim., 2012, vol. 50, n^o 1, p. 147–170.

http://dx.doi.org/10.1137/100799344
12Y. Chitour, P. Mason, M. Sigalotti.

On the marginal instability of linear switched systems, in: Systems & Control Letters, 2012, vol. 61, n^o 6, p. 747–757.

http://dx.doi.org/10.1016/j.sysconle.2012.04.005
13F. El Hachemi, M. Sigalotti, J. Daafouz.

Stability analysis of singularly perturbed switched linear systems, in: IEEE Trans. Automat. Control, 2012, vol. 57, p. 2116–2121.
14F. Hante, M. Sigalotti, M. Tucsnak.

On conditions for asymptotic stability of dissipative infinite-dimensional systems with intermittent damping, in: Journal of Differential Equations, May 2012, vol. 252, n^o 10, p. 5569-5593. [ DOI : 10.1016/j.jde.2012.01.037 ]

http://hal.inria.fr/inria-00616474

International Conferences with Proceedings

15A. Ajami, J.-F. Balmat, J.-P. Gauthier, T. Maillot.

Path Planning and Ground Control Station Simulator for UAV, in: Proceedings of the 2013 IEEE aerospace conference, 2013.
16U. Boscain, M. Caponigro, M. Sigalotti.

Controllability of the bilinear Schrödinger equation with several controls and application to a 3D molecule, in: Proceedings of the 51th IEEE Conference on Decision and Control, 2012.
17U. Boscain, R. Duits, F. Rossi, Y. Sachkov.

Curve cuspless reconstruction via sub-Riemannian geometry, in: Proceedings of the 51th IEEE Conference on Decision and Control, 2012.

http://arxiv.org/abs/1203.3089
18U. Boscain, F. Grönberg, R. Long, H. Rabitz.

Time minimal trajectories for two-level quantum systems with two bounded controls, in: Proceedings of the 51th IEEE Conference on Decision and Control, 2012.

http://arxiv.org/abs/1211.0666
19F. Chittaro, P. Mason, U. Boscain, M. Sigalotti.

Controllability of the Schroedinger equation via adiabatic methods and conical intersections of the eigenvalues, in: Proceedings of the 51th IEEE Conference on Decision and Control, 2012.

Scientific Popularization

20M. Lapert, Y. Zhang, M. Janich, S. J. Glaser, D. Sugny.

Une nouvelle métode pour optimiser le contraste en imagerie médicale, in: Actualités scientifiques du CNRS, 2012.

Other Publications

21D. Barilari, U. Boscain, R. W. Neel.

Small time heat kernel asymptotics at the sub-Riemannian cut locus, 2012.

http://hal.inria.fr/hal-00687651
22D. Barilari, J. Jendrej.

Small time heat kernel asymptotics at the cut locus on two-spheres of revolution.

http://arxiv.org/pdf/1211.1811v1.pdf
23U. Boscain, M. Caponigro, M. Sigalotti.

Controllability of the bilinear Schrödinger equation with several controls and application to a 3D molecule.

http://hal.inria.fr/hal-00691706
24U. Boscain, G. Charlot, R. Ghezzi.

Normal forms and invariants for 2-dimensional almost-Riemannian structures, 2012.

http://arxiv.org/abs/1008.5036

References in notes

25A. 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, n^o 3, p. 409–441.
26A. A. Agrachev, D. Liberzon.

Lie-algebraic stability criteria for switched systems, in: SIAM J. Control Optim., 2001, vol. 40, n^o 1, p. 253–269.

http://dx.doi.org/10.1137/S0363012999365704
27A. 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.
28A. A. Agrachev, A. V. Sarychev.

Navier-Stokes equations: controllability by means of low modes forcing, in: J. Math. Fluid Mech., 2005, vol. 7, n^o 1, p. 108–152.

http://dx.doi.org/10.1007/s00021-004-0110-1
29F. Albertini, D. D'Alessandro.

Notions of controllability for bilinear multilevel quantum systems, in: IEEE Trans. Automat. Control, 2003, vol. 48, n^o 8, p. 1399–1403.
30C. Altafini.

Controllability properties for finite dimensional quantum Markovian master equations, in: J. Math. Phys., 2003, vol. 44, n^o 6, p. 2357–2372.
31L. 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.
32G. Arechavaleta, J.-P. Laumond, H. Hicheur, A. Berthoz.

An optimality principle governing human locomotion, in: IEEE Trans. on Robotics, 2008, vol. 24, n^o 1.
33L. 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, n^o 3, p. 293–325.
34L. 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, n^o 1, p. 188–222.
35L. Baudouin, J. Salomon.

Constructive solution of a bilinear optimal control problem for a Schrödinger equation, in: Systems Control Lett., 2008, vol. 57, n^o 6, p. 453–464.

http://dx.doi.org/10.1016/j.sysconle.2007.11.002
36K. Beauchard.

Local controllability of a 1-D Schrödinger equation, in: J. Math. Pures Appl. (9), 2005, vol. 84, n^o 7, p. 851–956.
37K. Beauchard, J.-M. Coron.

Controllability of a quantum particle in a moving potential well, in: J. Funct. Anal., 2006, vol. 232, n^o 2, p. 328–389.
38M. Belhadj, J. Salomon, G. Turinici.

A stable toolkit method in quantum control, in: J. Phys. A, 2008, vol. 41, n^o 36, 362001, 10 p.

http://dx.doi.org/10.1088/1751-8113/41/36/362001
39F. Blanchini.

Nonquadratic Lyapunov functions for robust control, in: Automatica J. IFAC, 1995, vol. 31, n^o 3, p. 451–461.

http://dx.doi.org/10.1016/0005-1098(94)00133-4
40F. 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, n^o 3, p. 641–647.

http://dx.doi.org/10.1109/9.751368
41A. M. Bloch, R. W. Brockett, C. Rangan.

Finite Controllability of Infinite-Dimensional Quantum Systems, in: IEEE Trans. Automat. Control, 2010.
42V. D. Blondel, J. Theys, A. A. Vladimirov.

An elementary counterexample to the finiteness conjecture, in: SIAM J. Matrix Anal. Appl., 2003, vol. 24, n^o 4, p. 963–970.

http://dx.doi.org/10.1137/S0895479801397846
43A. 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.
44B. Bonnard, D. Sugny.

Time-minimal control of dissipative two-level quantum systems: the integrable case, in: SIAM J. Control Optim., 2009, vol. 48, n^o 3, p. 1289–1308.

http://dx.doi.org/10.1137/080717043
45A. Borzì, E. Decker.

Analysis of a leap-frog pseudospectral scheme for the Schrödinger equation, in: J. Comput. Appl. Math., 2006, vol. 193, n^o 1, p. 65–88.
46A. Borzì, U. Hohenester.

Multigrid optimization schemes for solving Bose-Einstein condensate control problems, in: SIAM J. Sci. Comput., 2008, vol. 30, n^o 1, p. 441–462.

http://dx.doi.org/10.1137/070686135
47U. Boscain.

Stability of planar switched systems: the linear single input case, in: SIAM J. Control Optim., 2002, vol. 41, n^o 1, p. 89–112.

http://dx.doi.org/10.1137/S0363012900382837
48C. 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.
49F. 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.
50R. 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, n^o 27, 275303, 9 p.

http://dx.doi.org/10.1088/1751-8113/42/27/275303
51G. Citti, A. Sarti.

A cortical based model of perceptual completion in the roto-translation space, in: J. Math. Imaging Vision, 2006, vol. 24, n^o 3, p. 307–326.

http://dx.doi.org/10.1007/s10851-005-3630-2
52J.-M. Coron.

Control and nonlinearity, Mathematical Surveys and Monographs, American Mathematical Society, Providence, RI, 2007, vol. 136, xiv+426 p.
53W. 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, n^o 4, p. 751–760.

http://dx.doi.org/10.1109/9.754812
54L. 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, Philadelphia, PA, 2000, vol. 2, p. xviii, 3–37.
55S. 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, p. 2111–2136.
56M. 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, n^o 6, p. 1327–1361.

http://dx.doi.org/10.1080/00207179508921959
57B. Franchi, R. Serapioni, F. Serra Cassano.

Regular hypersurfaces, intrinsic perimeter and implicit function theorem in Carnot groups, in: Comm. Anal. Geom., 2003, vol. 11, n^o 5, p. 909–944.
58M. Gugat.

Optimal switching boundary control of a string to rest in finite time, in: ZAMM Z. Angew. Math. Mech., 2008, vol. 88, n^o 4, p. 283–305.
59J. 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, p. 2655–2660.
60D. Hubel, T. Wiesel.

Brain and Visual Perception: The Story of a 25-Year Collaboration, Oxford University Press, Oxford, 2004.
61R. Illner, H. Lange, H. Teismann.

Limitations on the control of Schrödinger equations, in: ESAIM Control Optim. Calc. Var., 2006, vol. 12, n^o 4, p. 615–635.

http://dx.doi.org/10.1051/cocv:2006014
62A. Isidori.

Nonlinear control systems, Communications and Control Engineering Series, Second, Springer-Verlag, Berlin, 1989, xii+479 p, An introduction.
63K. Ito, K. Kunisch.

Optimal bilinear control of an abstract Schrödinger equation, in: SIAM J. Control Optim., 2007, vol. 46, n^o 1, p. 274–287.
64K. Ito, K. Kunisch.

Asymptotic properties of feedback solutions for a class of quantum control problems, in: SIAM J. Control Optim., 2009, vol. 48, n^o 4, p. 2323–2343.

http://dx.doi.org/10.1137/080720784
65F. Jean, G. Oriolo, M. Vendittelli.

A Globally Convergent Steering Algorithm for Regular Nonholonomic Systems, in: Proceedings of 44th IEEE CDC-ECC'05, Sevilla, Spain, 2005.
66R. Kalman.

When is a linear control system optimal?, in: ASME Transactions, Journal of Basic Engineering, 1964, vol. 86, p. 51–60.
67N. 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, n^o 3, part A, 032301, 11 p.
68N. Khaneja, B. Luy, S. J. Glaser.

Boundary of quantum evolution under decoherence, in: Proc. Natl. Acad. Sci. USA, 2003, vol. 100, n^o 23, p. 13162–13166.

http://dx.doi.org/10.1073/pnas.2134111100
69V. S. Kozyakin.

Algebraic unsolvability of a problem on the absolute stability of desynchronized systems, in: Avtomat. i Telemekh., 1990, p. 41–47.
70G. 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, p. 235-270.
71J.-S. Li, N. Khaneja.

Ensemble control of Bloch equations, in: IEEE Trans. Automat. Control, 2009, vol. 54, n^o 3, p. 528–536.

http://dx.doi.org/10.1109/TAC.2009.2012983
72D. Liberzon, J. P. Hespanha, A. S. Morse.

Stability of switched systems: a Lie-algebraic condition, in: Systems Control Lett., 1999, vol. 37, n^o 3, p. 117–122.

http://dx.doi.org/10.1016/S0167-6911(99)00012-2
73D. Liberzon.

Switching in systems and control, Systems & Control: Foundations & Applications, Birkhäuser Boston Inc., Boston, MA, 2003, xiv+233 p.
74H. Lin, P. J. Antsaklis.

Stability and stabilizability of switched linear systems: a survey of recent results, in: IEEE Trans. Automat. Control, 2009, vol. 54, n^o 2, p. 308–322.

http://dx.doi.org/10.1109/TAC.2008.2012009
75Y. Lin, E. D. Sontag, Y. Wang.

A smooth converse Lyapunov theorem for robust stability, in: SIAM J. Control Optim., 1996, vol. 34, n^o 1, p. 124–160.

http://dx.doi.org/10.1137/S0363012993259981
76W. Liu.

Averaging theorems for highly oscillatory differential equations and iterated Lie brackets, in: SIAM J. Control Optim., 1997, vol. 35, n^o 6, p. 1989–2020.

http://dx.doi.org/10.1137/S0363012994268667
77Y. Maday, J. Salomon, G. Turinici.

Monotonic parareal control for quantum systems, in: SIAM J. Numer. Anal., 2007, vol. 45, n^o 6, p. 2468–2482.

http://dx.doi.org/10.1137/050647086
78A. N. Michel, Y. Sun, A. P. Molchanov.

Stability analysis of discountinuous dynamical systems determined by semigroups, in: IEEE Trans. Automat. Control, 2005, vol. 50, n^o 9, p. 1277–1290.

http://dx.doi.org/10.1109/TAC.2005.854582
79M. Mirrahimi.

Lyapunov control of a particle in a finite quantum potential well, in: Proceedings of the 45th IEEE Conference on Decision and Control, 2006.
80M. Mirrahimi, P. Rouchon.

Controllability of quantum harmonic oscillators, in: IEEE Trans. Automat. Control, 2004, vol. 49, n^o 5, p. 745–747.
81A. 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, n^o 1, p. 59–64.

http://dx.doi.org/10.1016/0167-6911(89)90021-2
82R. 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.
83R. M. Murray, S. S. Sastry.

Nonholonomic motion planning: steering using sinusoids, in: IEEE Trans. Automat. Control, 1993, vol. 38, n^o 5, p. 700–716.

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84V. Nersesyan.

Growth of Sobolev norms and controllability of the Schrödinger equation, in: Comm. Math. Phys., 2009, vol. 290, n^o 1, p. 371–387.
85A. Y. Ng, S. Russell.

Algorithms for Inverse Reinforcement Learning, in: Proc. 17th International Conf. on Machine Learning, 2000, p. 663–670.
86J. Petitot.

Neurogéomètrie de la vision. Modèles mathématiques et physiques des architectures fonctionnelles, Les Éditions de l'École Polythecnique, 2008.
87J. Petitot, Y. Tondut.

Vers une neurogéométrie. Fibrations corticales, structures de contact et contours subjectifs modaux, in: Math. Inform. Sci. Humaines, 1999, n^o 145, p. 5–101.
88H. Rabitz, H. de Vivie-Riedle, R. Motzkus, K. Kompa.

Wither the future of controlling quantum phenomena?, in: SCIENCE, 2000, vol. 288, p. 824–828.
89D. Rossini, T. Calarco, V. Giovannetti, S. Montangero, R. Fazio.

Decoherence by engineered quantum baths, in: J. Phys. A, 2007, vol. 40, n^o 28, p. 8033–8040.

http://dx.doi.org/10.1088/1751-8113/40/28/S12
90P. Rouchon.

Control of a quantum particle in a moving potential well, in: Lagrangian and Hamiltonian methods for nonlinear control 2003, Laxenburg, IFAC, Laxenburg, 2003, p. 287–290.
91A. Sasane.

Stability of switching infinite-dimensional systems, in: Automatica J. IFAC, 2005, vol. 41, n^o 1, p. 75–78.

http://dx.doi.org/10.1016/j.automatica.2004.07.013
92A. 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, p. 2081–2086.
93M. 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.
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Stability criteria for switched and hybrid systems, in: SIAM Rev., 2007, vol. 49, n^o 4, p. 545–592.

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96E. Todorov.

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