Bibliography

Publications of the year

Articles in International Peer-Reviewed Journals

• 1M. Barbero-Liñán, M. Sigalotti.
  New high order sufficient conditions for configuration tracking, in: Automatica, 2015, vol. 62, pp. 222-226.
  https://hal.inria.fr/hal-01105126
• 2U. Boscain, G. Charlot, M. Gaye, P. Mason.
  Local properties of almost-Riemannian structures in dimension 3, in: Discrete and Continuous Dynamical Systems - Series A, September 2015, vol. 35, n^o 9. [ DOI : 10.3934/dcds.2015.35.4115 ]
  https://hal.inria.fr/hal-01247787
• 3U. Boscain, J.-P. Gauthier, F. Rossi, M. Sigalotti.
  Approximate controllability, exact controllability, and conical eigenvalue intersections for quantum mechanical systems, in: Communications in Mathematical Physics, February 2015, vol. 333, n^o 3, pp. 1225-1239. [ DOI : 10.1007/s00220-014-2195-6 ]
  https://hal.archives-ouvertes.fr/hal-00869706
• 4U. Boscain, P. Mason, G. Panati, M. Sigalotti.
  Controllability of spin-boson systems, in: Journal of Mathematical Physics, 2015, vol. 56.
  https://hal.inria.fr/hal-01132741
• 5Y. Chitour, M. Gaye, P. Mason.
  Geometric and asymptotic properties associated with linear switched systems, in: Journal of Differential Equations,, December 2015, vol. 259, n^o 11, pp. 5582-5616.
  https://hal.archives-ouvertes.fr/hal-01064241
• 6I. Haidar, P. Mason, M. Sigalotti.
  Converse Lyapunov-Krasovskii theorems for uncertain retarded differential equations, in: Automatica, 2015, vol. 62, pp. 263-273.
  https://hal.inria.fr/hal-00924252
• 7F. Jean, D. Prandi.
  Complexity of control-affine motion planning, in: SIAM Journal on Control and Optimization, April 2015, vol. 53, n^o 2, pp. 816-844, 29 pages. [ DOI : 10.1137/130950793 ]
  https://hal.archives-ouvertes.fr/hal-00909748
• 8T. Maillot, U. Boscain, J.-P. Gauthier, U. Serres.
  Lyapunov and Minimum-Time Path Planning for Drones, in: Journal of Dynamical and Control Systems, January 2015, vol. 21, n^o 1, pp. 1-34. [ DOI : 10.1007/s10883-014-9222-y ]
  https://hal.archives-ouvertes.fr/hal-01097155
• 9E. Paduro, M. Sigalotti.
  Approximate Controllability of the Two Trapped Ions System, in: Quantum Information Processing, 2015, vol. 14, pp. 2397-2418.
  https://hal.inria.fr/hal-01092509
• 10A. Rapaport, I. Haidar, J. Harmand.
  Global dynamics of the buffered chemostat for a general class of response functions, in: Journal of Mathematical Biology, July 2015, vol. 71, n^o 1, pp. 69-98. [ DOI : 10.1007/s00285-014-0814-7 ]
  https://hal.inria.fr/hal-00923826

International Conferences with Proceedings

• 11M. Barbero-Liñán, M. Sigalotti.
  Configuration Tracking for Mechanical Systems by Kinematic Reduction and Fast Oscillating Controls, in: 54th IEEE Conference on Decision and Control, Osaka, Japan, 2015.
  https://hal.inria.fr/hal-01216015
• 12D. Barilari, U. Boscain, E. Le Donne, M. Sigalotti.
  Time-Optimal Synthesis for Three Relevant Problems: The Brockett Integrator, the Grushin Plane and the Martinet Distribution, in: 54th IEEE Conference on Decision and Control, Osaka, Japan, 2015.
  https://hal.inria.fr/hal-01216012
• 13U. Boscain, J.-P. Gauthier, F. Rossi, M. Sigalotti.
  Equivalence between Exact and Approximate Controllability for Finite-Dimensional Quantum Systems, in: 54th IEEE Conference on Decision and Control, Osaka, Japan, 2015.
  https://hal.inria.fr/hal-01216023
• 14Y. Chitour, P. Mason, M. Sigalotti.
  Quasi-Barabanov Semigroups and Finiteness of the $L_2$-Induced Gain for Switched Linear Control Systems: Case of Full-State Observation, in: 54th IEEE Conference on Decision and Control, Osaka, Japan, 2015.
  https://hal.inria.fr/hal-01216017
• 15I. Haidar, P. Mason, S.-I. Niculescu, M. Sigalotti, A. Chaillet.
  Further remarks on Markus-Yamabe instability for time-varying delay differential equations, in: 12th IFAC Workshop on Time Delay Systems (TDS), Ann Arbor, United States, 2015.
  https://hal.inria.fr/hal-01215997
• 16E. Paduro, M. Sigalotti.
  Control of a Quantum Model for Two Trapped Ions, in: 54th IEEE Conference on Decision and Control, Osaka, Japan, 2015.
  https://hal.inria.fr/hal-01216018
• 17N. Pouradier Duteil, F. Rossi, U. Boscain, B. Piccoli.
  Developmental Partial Differential Equations, in: 54th IEEE Conference on Decision and Control, Osaka, Japan, 2015.
  https://hal.inria.fr/hal-01216030

Other Publications

• 18A. Agrachev, D. Barilari, L. Rizzi.
  Sub-Riemannian curvature in contact geometry, December 2015, to appear on Journal of Geometric Analysis.
  https://hal.archives-ouvertes.fr/hal-01160901
• 19A. 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
• 20D. Barilari, U. Boscain, E. L. Donne, M. Sigalotti.
  Sub-Finsler structures from the time-optimal control viewpoint for some nilpotent distributions, June 2015, 24 pages, 17 figures.
  https://hal.inria.fr/hal-01164043
• 21D. Barilari, L. Rizzi.
  On Jacobi fields and canonical connection in sub-Riemannian geometry, November 2015, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-01160902
• 22U. Boscain, R. Neel, L. Rizzi.
  Intrinsic random walks and sub-Laplacians in sub-Riemannian geometry, November 2015, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-01122735
• 23Y. Chitour, P. Mason, M. Sigalotti.
  A characterization of switched linear control systems with finite L2-gain, 2015, working paper or preprint.
  https://hal.inria.fr/hal-01198394
• 24Y. Chitour, G. Mazanti, M. Sigalotti.
  Stability of non-autonomous difference equations with applications to transport and wave propagation on networks, April 2015, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-01139814
• 25F. Colonius, G. Mazanti.
  Lyapunov exponents for random continuous-time switched systems and stabilizability, November 2015, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-01232164
• 26S. 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, 2015, 31 pages; this is the starting point for a living document - we welcome feedback and discussion.
  https://hal.inria.fr/hal-01216034
• 27D. Prandi, A. Remizov, R. Chertovskih, U. Boscain, J.-P. Gauthier.
  Highly corrupted image inpainting through hypoelliptic diffusion, February 2015, working paper or preprint.
  https://hal.inria.fr/hal-01139521

References in notes

• 28A. 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, pp. 409–441.
• 29A. A. Agrachev, D. Liberzon.
  Lie-algebraic stability criteria for switched systems, in: SIAM J. Control Optim., 2001, vol. 40, n^o 1, pp. 253–269.
  http://dx.doi.org/10.1137/S0363012999365704
• 30A. 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.
• 31A. 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, pp. 108–152.
  http://dx.doi.org/10.1007/s00021-004-0110-1
• 32F. Albertini, D. D'Alessandro.
  Notions of controllability for bilinear multilevel quantum systems, in: IEEE Trans. Automat. Control, 2003, vol. 48, n^o 8, pp. 1399–1403.
• 33C. Altafini.
  Controllability properties for finite dimensional quantum Markovian master equations, in: J. Math. Phys., 2003, vol. 44, n^o 6, pp. 2357–2372.
• 34L. 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.
• 35G. 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.
• 36L. 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, pp. 293–325.
• 37L. 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, pp. 188–222.
• 38L. 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, pp. 453–464.
  http://dx.doi.org/10.1016/j.sysconle.2007.11.002
• 39K. Beauchard.
  Local controllability of a 1-D Schrödinger equation, in: J. Math. Pures Appl. (9), 2005, vol. 84, n^o 7, pp. 851–956.
• 40K. Beauchard, J.-M. Coron.
  Controllability of a quantum particle in a moving potential well, in: J. Funct. Anal., 2006, vol. 232, n^o 2, pp. 328–389.
• 41M. 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
• 42F. Blanchini.
  Nonquadratic Lyapunov functions for robust control, in: Automatica J. IFAC, 1995, vol. 31, n^o 3, pp. 451–461.
  http://dx.doi.org/10.1016/0005-1098(94)00133-4
• 43F. 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, pp. 641–647.
  http://dx.doi.org/10.1109/9.751368
• 44A. M. Bloch, R. W. Brockett, C. Rangan.
  Finite Controllability of Infinite-Dimensional Quantum Systems, in: IEEE Trans. Automat. Control, 2010.
• 45V. 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, pp. 963–970.
  http://dx.doi.org/10.1137/S0895479801397846
• 46A. 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.
• 47B. 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, pp. 1289–1308.
  http://dx.doi.org/10.1137/080717043
• 48A. 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, pp. 65–88.
• 49A. Borzì, U. Hohenester.
  Multigrid optimization schemes for solving Bose-Einstein condensate control problems, in: SIAM J. Sci. Comput., 2008, vol. 30, n^o 1, pp. 441–462.
  http://dx.doi.org/10.1137/070686135
• 50C. 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.
• 51F. Bullo, A. D. Lewis.
  Geometric control of mechanical systems, Texts in Applied Mathematics, Springer-Verlag, New York, 2005, vol. 49, xxiv+726 p.
• 52R. 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
• 53G. 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, pp. 307–326.
  http://dx.doi.org/10.1007/s10851-005-3630-2
• 54J.-M. Coron.
  Control and nonlinearity, Mathematical Surveys and Monographs, American Mathematical Society, Providence, RI, 2007, vol. 136, xiv+426 p.
• 55W. 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, pp. 751–760.
  http://dx.doi.org/10.1109/9.754812
• 56L. 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.
• 57S. 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.
• 58M. 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, pp. 1327–1361.
  http://dx.doi.org/10.1080/00207179508921959
• 59B. 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, pp. 909–944.
• 60M. 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, pp. 283–305.
• 61J. 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.
• 62D. Hubel, T. Wiesel.
  Brain and Visual Perception: The Story of a 25-Year Collaboration, Oxford University Press, Oxford, 2004.
• 63R. Illner, H. Lange, H. Teismann.
  Limitations on the control of Schrödinger equations, in: ESAIM Control Optim. Calc. Var., 2006, vol. 12, n^o 4, pp. 615–635.
  http://dx.doi.org/10.1051/cocv:2006014
• 64A. Isidori.
  Nonlinear control systems, Communications and Control Engineering Series, Second, Springer-Verlag, Berlin, 1989, xii+479 p, An introduction.
• 65K. Ito, K. Kunisch.
  Optimal bilinear control of an abstract Schrödinger equation, in: SIAM J. Control Optim., 2007, vol. 46, n^o 1, pp. 274–287.
• 66K. 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, pp. 2323–2343.
  http://dx.doi.org/10.1137/080720784
• 67R. Kalman.
  When is a linear control system optimal?, in: ASME Transactions, Journal of Basic Engineering, 1964, vol. 86, pp. 51–60.
• 68N. 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.
• 69N. Khaneja, B. Luy, S. J. Glaser.
  Boundary of quantum evolution under decoherence, in: Proc. Natl. Acad. Sci. USA, 2003, vol. 100, n^o 23, pp. 13162–13166.
  http://dx.doi.org/10.1073/pnas.2134111100
• 70V. S. Kozyakin.
  Algebraic unsolvability of a problem on the absolute stability of desynchronized systems, in: Avtomat. i Telemekh., 1990, pp. 41–47.
• 71G. 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.
• 72J.-S. Li, N. Khaneja.
  Ensemble control of Bloch equations, in: IEEE Trans. Automat. Control, 2009, vol. 54, n^o 3, pp. 528–536.
  http://dx.doi.org/10.1109/TAC.2009.2012983
• 73D. 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, pp. 117–122.
  http://dx.doi.org/10.1016/S0167-6911(99)00012-2
• 74D. Liberzon.
  Switching in systems and control, Systems & Control: Foundations & Applications, Birkhäuser Boston Inc., Boston, MA, 2003, xiv+233 p.
• 75H. 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, pp. 308–322.
  http://dx.doi.org/10.1109/TAC.2008.2012009
• 76Y. 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, pp. 124–160.
  http://dx.doi.org/10.1137/S0363012993259981
• 77W. Liu.
  Averaging theorems for highly oscillatory differential equations and iterated Lie brackets, in: SIAM J. Control Optim., 1997, vol. 35, n^o 6, pp. 1989–2020.
  http://dx.doi.org/10.1137/S0363012994268667
• 78Y. Maday, J. Salomon, G. Turinici.
  Monotonic parareal control for quantum systems, in: SIAM J. Numer. Anal., 2007, vol. 45, n^o 6, pp. 2468–2482.
  http://dx.doi.org/10.1137/050647086
• 79A. 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, pp. 1277–1290.
  http://dx.doi.org/10.1109/TAC.2005.854582
• 80M. Mirrahimi.
  Lyapunov control of a particle in a finite quantum potential well, in: Proceedings of the 45th IEEE Conference on Decision and Control, 2006.
• 81M. Mirrahimi, P. Rouchon.
  Controllability of quantum harmonic oscillators, in: IEEE Trans. Automat. Control, 2004, vol. 49, n^o 5, pp. 745–747.
• 82A. 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, pp. 59–64.
  http://dx.doi.org/10.1016/0167-6911(89)90021-2
• 83R. 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.
• 84R. M. Murray, S. S. Sastry.
  Nonholonomic motion planning: steering using sinusoids, in: IEEE Trans. Automat. Control, 1993, vol. 38, n^o 5, pp. 700–716.
  http://dx.doi.org/10.1109/9.277235
• 85V. Nersesyan.
  Growth of Sobolev norms and controllability of the Schrödinger equation, in: Comm. Math. Phys., 2009, vol. 290, n^o 1, pp. 371–387.
• 86A. Y. Ng, S. Russell.
  Algorithms for Inverse Reinforcement Learning, in: Proc. 17th International Conf. on Machine Learning, 2000, pp. 663–670.
• 87J. Petitot.
  Neurogéomètrie de la vision. Modèles mathématiques et physiques des architectures fonctionnelles, Les Éditions de l'École Polythechnique, 2008.
• 88J. Petitot, Y. Tondut.
  Vers une neurogéométrie. Fibrations corticales, structures de contact et contours subjectifs modaux, in: Math. Inform. Sci. Humaines, 1999, n^o 145, pp. 5–101.
• 89H. Rabitz, H. de Vivie-Riedle, R. Motzkus, K. Kompa.
  Wither the future of controlling quantum phenomena?, in: SCIENCE, 2000, vol. 288, pp. 824–828.
• 90D. Rossini, T. Calarco, V. Giovannetti, S. Montangero, R. Fazio.
  Decoherence by engineered quantum baths, in: J. Phys. A, 2007, vol. 40, n^o 28, pp. 8033–8040.
  http://dx.doi.org/10.1088/1751-8113/40/28/S12
• 91P. 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.
• 92A. Sasane.
  Stability of switching infinite-dimensional systems, in: Automatica J. IFAC, 2005, vol. 41, n^o 1, pp. 75–78.
  http://dx.doi.org/10.1016/j.automatica.2004.07.013
• 93A. 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.
• 94M. 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.
• 95R. Shorten, F. Wirth, O. Mason, K. Wulff, C. King.
  Stability criteria for switched and hybrid systems, in: SIAM Rev., 2007, vol. 49, n^o 4, pp. 545–592.
  http://dx.doi.org/10.1137/05063516X
• 96H. 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.
• 97E. Todorov.
  12, in: Optimal control theory, Bayesian Brain: Probabilistic Approaches to Neural Coding, Doya K (ed), 2006, pp. 269–298.
• 98G. 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.
• 99L. Yatsenko, S. Guérin, H. Jauslin.
  Topology of adiabatic passage, in: Phys. Rev. A, 2002, vol. 65, 043407, 7 p.
• 100E. Zuazua.
  Switching controls, in: Journal of the European Mathematical Society, 2011, vol. 13, n^o 1, pp. 85–117.