Free access
Issue
ESAIM: COCV
Volume 13, Number 2, April-June 2007
Page(s) 207 - 236
DOI http://dx.doi.org/10.1051/cocv:2007012
Published online 12 May 2007
  1. A.A. Agrachev and R.V. Gamkrelidze, Second order optimality condition for the time optimal problem. Matem. Sbornik 100 (1976) 610–643. English transl. in: Math. USSR Sbornik 29 (1976) 547–576.
  2. A.A. Agrachev and R.V. Gamkrelidze, Symplectic geometry for optimal control, Nonlinear controllability and optimal control. Dekker, New York, Monogr. Textbooks Pure Appl. Math. 133 (1990) 263–277.
  3. A.A. Agrachev and Yu.L. Sachkov, Control theory from the geometric viewpoint, Encyclopedia of Mathematical Sciences, 87. Control Theory and Optimization, II. Springer-Verlag, Berlin (2004) 412 pp.
  4. A.A. Agrachev and A.V. Sarychev, Abnormal sub-Riemannian geodesics: Morse index and rigidity. Ann. Inst. Henri Poincaré 13 (1996) 635–690.
  5. A.A. Agrachev and A.V. Sarychev, On abnormal extremals for Lagrange variational problems. J. Math. Syst. Estim. Cont. 8 (1998) 87–118.
  6. C. Bischof, A. Carle, P. Kladem and A. Mauer, Adifor 2.0: Automatic Differentiation of Fortran 77 Programs. IEEE Comput. Sci. Engrg. 3 (1996) 18–32. [CrossRef]
  7. O. Bolza, Calculus of variations. Chelsea Publishing Co., New York (1973).
  8. B. Bonnard, Feedback equivalence for nonlinear systems and the time optimal control problem. SIAM J. Control Optim. 29 (1991) 1300–1321. [CrossRef] [MathSciNet]
  9. B. Bonnard and J.-B. Caillau, Introduction to nonlinear optimal control, in Advances Topics in Control Systems Theory, Lecture Notes from FAP 2004, F. Lamnabhi-Lagarrigue, A. Loria, E. Panteley Eds., Springer, Berlin (2005).
  10. B. Bonnard and M. Chyba, The role of singular trajectories in control theory. Springer Verlag, New York (2003).
  11. B. Bonnard and I. Kupka, Théorie des singularités de l'application entrée/sortie et optimalité des trajectoires singulières dans le problème du temps minimal. Forum Math. 5 (1993) 111–159. [CrossRef] [MathSciNet]
  12. B. Bonnard, J.-B. Caillau and E. Trélat, Geometric optimal control of elliptic Keplerian orbits. Discrete Contin. Dyn. Syst. 5 (2005) 929–956. [CrossRef] [MathSciNet]
  13. B. Bonnard, J.-B. Caillau and E. Trélat, Cotcot: short reference manual, ENSEEIHT-IRIT Technical Report RT/APO/05/1 (2005) www.n7.fr/apo/cotcot.
  14. J.B. Caillau, J. Noailles and J. Gergaud, 3D Geosynchronous Transfer of a Satellite: Continuation on the Thrust. J. Opt. Theory Appl. 118 (2003) 541–565. [CrossRef]
  15. Y. Chitour, F. Jean and E. Trélat, Genericity results for singular trajectories. J. Diff. Geom. 73 (2006) 45–73.
  16. J. de Morant, Contrôle en temps minimal des réacteurs chimiques discontinus. Ph.D. Thesis, Univ. Rouen (1992).
  17. S. Galot, D. Hulin and J. Lafontaine, Riemannian geometry. Springer-Verlag, Berlin (1987).
  18. B.S. Goh, Necessary conditions for singular extremals involving multiple control variables. SIAM J. Cont. 4 (1966) 716–731. [CrossRef] [MathSciNet]
  19. M.R. Hestenes, Application of the theory of quadratic forms in Hilbert spaces to the calculus of variations. Pac. J. Math. 1 (1951) 525–582.
  20. M.R. Hestenes, Optimization theory – the finite dimensional case. Wiley (1975).
  21. A.D. Ioffe and V.M. Tikhomirov, Theory of extremal problems. North-Holland Publishing Co., Amsterdam (1979).
  22. H.J. Kelley, R. Kopp and H.G. Moyer, Singular extremals, in Topics in optimization, G. Leitman Ed., Academic Press, New York (1967) 63–101.
  23. A.J. Krener, The high-order maximum principle and its applications to singular extremals. SIAM J. Cont. Opt. 15 (1977) 256–293. [CrossRef]
  24. L. Pontryagin, V. Boltyanskii, R. Gamkrelidze and E. Mischenko, The mathematical theory of optimal processes. Wiley Interscience (1962).
  25. A.V. Sarychev, The index of second variation of a control system. Matem. Sbornik 113 (1980) 464–486. English transl. in: Math. USSR Sbornik 41 (1982) 383–401.
  26. L.F. Shampine, H.A. Watts and S. Davenport, Solving non-stiff ordinary differential equations – the state of the art. Technical Report sand75-0182, Sandia Laboratories, Albuquerque, New Mexico (1975).
  27. E. Trélat, Asymptotics of accessibility sets along an abnormal trajectory. ESAIM: COCV 6 (2001) 387–414. [CrossRef] [EDP Sciences]
  28. L.C. Young, Lectures on the calculus of variations and optimal control theory. Chelsea, New York (1980).
  29. O. Zarrouati, Trajectoires spatiales. CNES-Cepadues, Toulouse (1987).