Free Access
Issue
ESAIM: COCV
Volume 17, Number 1, January-March 2011
Page(s) 267 - 292
DOI https://doi.org/10.1051/cocv/2010004
Published online 24 March 2010
  1. A.A. Agrachev and Y.L. Sachkov, Control theory from the geometric viewpoint, Encyclopaedia of Mathematical Sciences 87, Control Theory and Optimization II. Springer-Verlag, Berlin, Germany (2004). [Google Scholar]
  2. E.L. Allgower and K.G. Georg, Introduction to numerical continuation methods, SIAM Classics in Applied Maths 45. Society for Industrial and Applied Mathematics, Philadelphia, USA (2003). [Google Scholar]
  3. D. Bao, C. Robles and Z. Shen, Zermelo navigation on Riemannian manifolds. J. Differential Geom. 66 (2004) 377–435. [MathSciNet] [Google Scholar]
  4. A.G. Bliss, Lectures on the Calculus of Variations. University of Chicago Press, Chicago, USA (1946). [Google Scholar]
  5. B. Bonnard and I. Kupka, Théorie des singularités de l'application entrée/sortie et optimalité des trajectoires singulières dans le problème du temps minimal [Theory of the singularities of the input/output mapping and optimality of singular trajectories in the minimal-time problem]. Forum Math. 5 (1993) 111–159. [CrossRef] [MathSciNet] [Google Scholar]
  6. B. Bonnard and D. Sugny, Time-minimal control of dissipative two-level quantum systems: the integrable case. SIAM J. Control Optim. 48 (2009) 1289–1308. [CrossRef] [MathSciNet] [Google Scholar]
  7. B. Bonnard and D. Sugny, Geometric optimal control and two-level dissipative quantum systems. Control Cybern. (to appear). [Google Scholar]
  8. B. Bonnard, L. Faubourg and E. Trélat, Mécanique céleste et contrôle des véhicules spatiaux. Springer, Berlin, Germany (2005). [Google Scholar]
  9. B. Bonnard, R. Dujol and J.-B. Caillau, Smooth approximations of single-input controlled Keplerian trajectories: homotopies and averaging, in Taming heterogeneity and complexity of embedded control, Proceedings of the Joint CTS-HYCON Workshop on Nonlinear and Hybrid Control, Paris, France (2006) 73–95. [Google Scholar]
  10. B. Bonnard, J.-B. Caillau and E. Trélat, Second order optimality conditions in the smooth case and applications in optimal control. ESAIM: COCV 13 (2007) 207–236. [CrossRef] [EDP Sciences] [Google Scholar]
  11. B. Bonnard, J.-B. Caillau, R. Sinclair and M. Tanaka, Conjugate and cut loci of a two-sphere of revolution with application to optimal control. Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009) 1081–1098. [CrossRef] [MathSciNet] [Google Scholar]
  12. B. Bonnard, M. Chyba and D. Sugny, Time-minimal control of dissipative two-level quantum systems: the generic case. IEEE Trans. Automat. Contr. 54 (2009) 2595–2610. [Google Scholar]
  13. B. Bonnard, O. Cots, N. Shcherbakova and D. Sugny, The energy minimization problem for two-level dissipative quantum systems. J. Math. Phys. (to appear). [Google Scholar]
  14. U. Boscain and P. Mason, Time minimal trajectories for a spin 1/2 particle in a magnetic field. J. Math. Phys. 47 (2006) 062101. [CrossRef] [MathSciNet] [Google Scholar]
  15. H.-P. Breuer and F. Petruccione, The theory of open quantum systems. Oxford University Press, London, UK (2002). [Google Scholar]
  16. D. D'Alessandro, Introduction to quantum control and dynamics, Applied Mathematics and Nonlinear Science Series. Chapman & Hall/CRC, Boca Raton, USA (2008). [Google Scholar]
  17. M.P. do Carmo, Riemannian geometry. Birkhauser, Boston, USA (1992). [Google Scholar]
  18. R. Dujol, Contribution du contrôle orbital des transferts mono-entrée en mécanique spatiale. Ph.D. Thesis, ENSEEIHT-INP, France (2006). [Google Scholar]
  19. J. Gergaud and T. Haberkorn, Homotopy method for minimum consumption orbit transfer problem. ESAIM: COCV 12 (2006) 294–310. [CrossRef] [EDP Sciences] [Google Scholar]
  20. T. Haberkhorn, Transfert orbital avec minimisation de la consommation : résolution par homotopie différentielle. Ph.D. Thesis, ENSEEIHT-INP, France (2004). [Google Scholar]
  21. N. Khaneja, R. Brockett and S.J. Glaser, Time optimal control of spin systems. Phys. Rev. A. 63 (2001) 032308. [Google Scholar]
  22. N. Khaneja, S.J. Glaser and R. Brockett, Sub-Riemannian geometry and time optimal control of three spin systems: quantum gates and coherence transfer. Phys. Rev. A (3) 65 (2002) 032301. [CrossRef] [MathSciNet] [Google Scholar]
  23. D.F. Lawden, Elliptic functions and applications. Springer Verlag, New York, USA (1989). [Google Scholar]
  24. H. Maurer and H.J. Oberle, Second order sufficient conditions for optimal control problems with free final time: the Riccati approach. SIAM J. Control Optim. 41 (2002) 380–403. [CrossRef] [MathSciNet] [Google Scholar]
  25. L.S. Pontryagin, V.G. Boltyanskii, R.V. Gamkrelidze and E.F. Mishchenko, The mathematical theory of optimal processes. L.W. Neustadt Interscience Publishers, John Wiley & Sons, Inc., New York-London (1962). [Google Scholar]
  26. A. Sarychev, The index of the second variation of a control system. Math. Sbornik 41 (1982) 383–401. [CrossRef] [Google Scholar]
  27. T. Schulte-Herbrüggen, A.K. Spörl, R. Marx, N. Khaneja, J.M. Myers, A.F. Fahmy and S.J. Glaser, Quantum computing implemented via optimal control: Theory and application to spin and pseudo-spin systems, in Lectures on quantum information, D. Bruß and G. Leuchs Eds., Wiley-VCH (2006) 481. [Google Scholar]
  28. T. Vieillard, F. Chaussard, D. Sugny, B. Lavorel and O. Faucher, Field-free molecular alignment of CO2 mixtures in presence of collisional relaxation. J. Raman Spec. 39 (2008) 694. [CrossRef] [Google Scholar]
  29. R. Wu, A. Pechen, H. Rabitz, M. Hsieh and B. Tsou, Control landscapes for observable preparation with open quantum systems. J. Math. Phys. 49 (2008) 022108. [CrossRef] [MathSciNet] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.