Notes on Sub-Riemannian Geometry


Book Editor

Chapters of Books


Papers in Refereed Journals:

[53] D. Barilari, U. Boscain, E. Le Donne, M. Sigalotti, Sub-Finsler structures from the time-optimal control viewpoint for some nilpotent distributions To appear on Journal of Dynamical and Control Systems.

[52] S. Glaser, U. Boscain, T. Calarco, C. Koch, W. Kckenberger, R. Kosloff, I. Kuprov, B. Luy, S. Schirmer, T. Schulte-Herbrggen, D. Sugny, F. Wilhelm Training Schrdinger's cat: quantum optimal control Eur. Phys. J. D (2015) 69: 279.

[51] D. Barilari, U. Boscain, G. Charlot, R.W. Neel, On the heat diffusion for generic Riemannian and sub-Riemannian structures To appear on International Mathematics Research Notices.

[50] U. Boscain, P. Mason, G. Panati, M. Sigalotti, On the control of spin-boson systems. J. Math. Phys. 56 (2015), no. 9, 092101, 15 pp.

[49] U. Boscain, D. Prandi, M. Seri, Spectral analysis and the Aharonov-Bohm effect on certain almost-Riemannian manifolds. to appear on Communication on PDEs.

[48] U. Boscain, D. Prandi, Self-adjoint extensions and stochastic completeness of the Laplace-Beltrami operator on conic and anticonic surfaces anticonic-type surfaces J. Differential Equations 260 (2016) 32343269

[47] U. Boscain, G. Charlot, M. Gaye, P. Mason, Local properties of almost-Riemannian structures in dimension 3. Discrete and Continuous Dynamical Systems Volume 35, Issue 9, 2015 Pages 4115-4147

[46] U. Boscain, J.P. Gauthier, F. Rossi M. Sigalotti, Approximate controllability, exact controllability, and conical eigenvalue intersections for quantum mechanical systems.. Comm. Math. Phys. 333 (2015), no. 3, 1225-1239.

[45] U. Boscain, F. Gronberg, R. Long, H. Rabitz, Time minimal trajectories for two-level quantum systems with two bounded controls. J. Math. Phys. 55 , 062106 (2014) ;

[44] T. Maillot, U. Boscain, J.P. Gauthier, U. Serres. Lyapunov and minimum-time path planning for drones. J. Dyn. Control Syst. 21 (2015), no. 1, 4780.

[43] U. Boscain, R. Chertovskih, J.P. Gauthier, A. Remizov. Hypoelliptic diffusion and human vision: a semi-discrete new twist. SIAM Journal on Imaging Sciences 2014, Vol. 7, No. 2, pp. 669-695

[42] R. Duits, U. Boscain, F. Rossi, Y. Sachkov. Association fields via cuspless sub-Riemannian geodesics in SE(2). Journal of Mathematical Imaging and Vision June 2014, Volume 49, Issue 2, pp 384-417.

[41] U. Boscain, R. Duits, F. Rossi, Y. Sachkov. Curve cuspless reconstruction via sub-Riemannian geometry Accepted on ESAIM: Control, Optimization and Calculus of Variations (COCV), Volume 20, Issue 03, 2014, pp 748 - 770.

[40] U. Boscain, M.Caponigro, Mario Sigalotti Multi-input Schrdinger equation: controllability, tracking, and application to the quantum angular momentum. Journal of Differential Equations 256 (2014), no. 11, 3524-3551.

[39] U. Boscain, J.P. Gauthier. On the Spherical Hausdorff Measure in Step 2, Corank 2 sub-Riemannian Geometry. SIAM J. Control Optim. 51 (2013), no. 6, 4450-4462.

[38] D. Barilari, U. Boscain, R. Neel, Small time heat kernel asymptotics at the sub-Riemannian cut locus. JDG Vol 92, No.3, 2012, pp. 373-416.

[37] D. Barilari, U. Boscain, J.P. Gauthier, On 2-step, corank 2 nilpotent sub-Riemannian metrics . SIAM J. CONTROL OPTIM, Vol. 50, No. 1, pp. 559--582.

[36] U. Boscain, C. Laurent, The Laplace-Beltrami operator in almost-Riemannian Geometry. Ann. Inst. Fourier (Grenoble) 63 (2013), no. 5, 1739-1770.

[35] U. Boscain, F. Chittaro, P. Mason, M. Sigalotti, Adiabatic control of the Schroedinger equation via conical intersections of the eigenvalues. IEEE Transactions on Automatic Control, Volume: 57, Issue: 8, pp. 1970 - 1983, 2012.

[34] U. Boscain, M. Caponigro, T. Chambrion, and M. Sigalotti, A weak spectral condition for the controllability of the bilinear Schrdinger equation with application to the control of a rotating planar molecule. Commun. Math. Phys. 311, 423-455 (2012).

[33] U. Boscain, G. Charlot, R. Ghezzi, Normal forms and invariants for 2-dimensional almost-Riemannian structures. Differential Geometry and its Applications.Vol. 31, No. 1, 2013, Pages 41-62.

[32] U. Boscain, J. Duplaix, J.P. Gauthier, F. Rossi, Anthropomorphic image reconstruction via hypoelliptic diffusion. SIAM J. CONTROL OPTIM.Vol. 50, No. 3, pp. 1309--1336

[31] A. Agrachev, D. Barilari, U. Boscain, On the Hausdorff volume in sub-Riemannian geometry. Calculus of Variations and PDE's Volume 43, Numbers 3-4 March 2012.

[30] U. Boscain, J.P. Gauthier, F. Rossi ``Hypoelliptic heat kernel over 3-step nilpotent Lie groups'' , to appear on Contemporary Mathematics. Fundamental Directions.

[29] U. Boscain, G. Charlot, R. Ghezzi, M. Sigalotti, Lipschitz Classification of Almost-Riemannian Distances on Compact Oriented Surfaces. J. Geom. Anal. 23 (2013), no. 1, 438455. September 2011. DOI 10.1007/s12220-011-9262-4.

[28] A. Agrachev, U. Boscain, G. Charlot, R. Ghezzi, M. Sigalotti, Two-Dimensional Almost-Riemannian Structures with Tangency Points, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, Volume 27, Issue 3, May-June 2010, Pages 793-807

[27] U. Boscain, G. Charlot, F. Rossi, ``Existence of planar curves minimizing length and curvature'' , Proceedings of the Steklov Institute of Mathematics, 2010, Vol. 270, pp. 43--56.

[26] M. Balde, U. Boscain, P. Mason, "A note on stability conditions for planar switched systems". International Journal of Control, Vol 82, 2009, pp. 1882-1888.

[25] U. Boscain, F. Rossi, ``Projective Reed-Shepp Car on $S^2$'', ESAIM: Control, Optimization and Calculus of Variations (COCV), 2010, pp. 275-297, DOI: 10.1051/cocv:2008075

[24] A. Agrachev, U. Boscain, J.P. Gauthier, F. Rossi, ``The intrinsic hypoelliptic Laplacian and the corresponding heat kernel on unimodular Lie groups'' Journal of Functional Analysis, Volume 256, Issue 8, 15 April 2009, Pages 2621-2655.

[23] T. Chambrion, P. Mason, M. Sigalotti and U. Boscain, Controllability of the discrete-spectrum Schroedinger equation driven by an external field, Annales de l'Institut Henri Poincare (C) Non Linear Analysis Volume 26, Issue 1, January-February 2009, Pages 329-349.

[22] U. Boscain, F. Rossi, ``Invariant Carnot-Caratheodory metrics on S^3, SO(3), SL(2) and Lens Spaces'', SIAM, Journal on Control and Optimization, Vol 47, pp. 1851-1878, (2008).

[21] U. Boscain, S. Polidoro, Gaussian estimates for hypoelliptic operators via optimal control Rendiconti dei Lincei, Matematica ed Applicazioni Vol 18, Nov. 2007.

[20] U. Boscain, M. Sigalotti, High-order angles in almost-Riemannian geometry, Actes du seminaire de theorie spectrale et geometrie. Grenoble. Vol 25, 2006-2007, pp. 41-54.

[19] A. Agrachev, U. Boscain, M. Sigalotti, ``A Gauss-Bonnet-like Formula on Two-Dimensional Almost-Riemannian Manifolds'', Discrete and Continuous Dynamical Systems-A, vol. 20, pp. 801-822, 2008.

[18] M. Balde, U. Boscain, ``Stability of Planar Switched Systems: the Nondiagonalizable Case'', Communication on Pure and Applied Analysis Vol. 7, N. 1, pp. 1--21, (2008).

[17]Paolo Mason, Rebecca Salmoni, Ugo Boscain, Yacine Chitour, Limit Time Optimal Syntheses for a control-affine system on $S^2$, SIAM, Journal on Control and Optimization, vol. 47, pp. 111--143 (2008).

[16] U. Boscain, P. Mason, ``Time Minimal Trajectories for a Spin 1/2 Particle in a Magnetic field '', J. Math. Phys. 47, 062101 (2006) (29 pages).

[15] P. Mason, U. Boscain, Y. Chitour, ``Common Polynomial Lyapunov Functions for Linear Switched Systems'', SIAM SICON, Journal on Control and Optimization, Vol. 45, n. 1, pages 226 - 245

[14] U. Boscain, G. Charlot, M. Sigalotti, `` Stability of Planar Nonlinear Switched Systems , DCDS-A, Vol 15, n.2, June 2006, pp. 415-432.

[13] U. Boscain, T. Chambrion, G. Charlot, ``Nonisotropic 3-level Quantum Systems: Complete Solutions for Minimum Time and Minimal Energy'', Discrete and Continuous Dynamical Systems-B, Vol. 5, n. 4, pp. 957 -- 990 (2005).

[12] U. Boscain, Y. Chitour, Time Optimal Synthesis for Left--Invariant Control Systems on SO(3), SIAM SICON, Journal on Control and Optimization, Vol. 44, No. 1 pp. 111-139, 2005.

[11] U. Boscain, I. Nikolaev, B. Piccoli, ``Classification of Stable Time--Optimal Controls on 2-manifolds'', Journal of Mathematical Sciences. Vol. 135, Number 4, pp. 3109-3124. (2006). Published in Russian on Sovrem. Mat. Prilozh. No. 21, Geom. Zadachi Teor. Upr. (2004), pp. 19--35.

[10] U. Boscain, G. Charlot, Resonance of Minimizers for $n$-level Quantum Systems with an Arbitrary Cost, ESAIM: Control, Optimisation and Calculus of Variations (COCV), VOL.10, pp. 593-614 (2004).

[9] U. Boscain, T. Chambrion, J-P Gauthier, On the K+P problem for a three-level quantum system: optimality implies resonance, Journal of Dynamical and Control Systems n. 8, pp.547--572 (2002)

[8] U. Boscain, Gregoire Charlot, Jean-Paul Gauthier, Stephane Guerin, Hans--Rudolf Jauslin, Optimal Control in laser-induced population transfer for two- and three-level quantum systems (.ps), Journal of Mathematical Physics, n. 43, pp. 2107--2132 (2002)

[7] U. Boscain, Y.Chitour, On the minimum time problem for driftless left-invariant control systems on SO(3) (.ps), Communication on Pure and Applied Analysis, n. 1 pp. 285--312 (2002)

[6] U. Boscain, Stability of Planar Switched Systems: the linear Single Input Case (.ps) SIAM SICON, Journal on Control and Optimization, n. 41 pp.89--112. (2002)
REMARK: the conditions in the RCcase given in the paper [6] are not correct. For the corrected statment and proof of the RCcase, see the paper: P. Mason, U. Boscain, Y.Chitour, ``Common Polynomial Lyapunov Functions for Linear Switched Systems'', Preprint SISSA 52/2004/M,
[5] U. Boscain and B. Piccoli, On Automaton Recognizability of Abnormal Extremals (.ps), SIAM SICON, Journal on Control and Optimization, n. 40, pp. 1333--1357 (2002)

[4] U. Boscain, Projection singularities of extremals and Morse property for minimum time, Proceedings of the Steklov Mathematical Institute, n. 236, pp.399-407 (2002)

[3] U. Boscain, B. Piccoli, Morse Properties for the Minimum Time Function on 2--D Manifolds (.ps), Journal of Dynamical and Control Systems, Vol.7 (2001), no. 3, 385--423.

[2] U. Boscain and B. Piccoli, Extremal Synthesis for Generic Planar Systems (.ps) Journal of Dynamical and Control Systems, Vol.7 (2001), no. 2, 209--258 (.pdf)

[1] U. Boscain, B. Piccoli, Geometric Control Approach To Synthesis Theory, (.ps) Rendiconti del Seminario Matematico dell'Universita e del Politecnico di Torino, Torino, 1998, V.56, 4 (1998), pp. 53-67.

Papers in Refereed Conference Proceedings:


Poly d'automatique

U. Boscain, Y. Chitour Introduction a' l'automatique (French)