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ArticleOriginal scientific text

Title

Casimir elements and optimal control

Authors 1

Affiliations

  1. Department of Mathematics, University of Toronto, 100, St George Street, Toronto, Ontario, M5S 1A1 Canada

Bibliography

  1. V. I. Arnold, Méthodes Mathématiques de la Mécanique Classique, Editions Mir, 1976.
  2. B. Bonnard, V. Jurdjevic, I. A. K. Kupka and G. Sallet, Transitivity of families of vector fields on the semi-direct products of Lie groups, Trans. Amer. Math. Soc. 275 (1982), 525-535.
  3. J. D. Boissonat, A. Cereso, and J. LeBlond, On shortest paths in the plane subject to a constraint on the derivative of the curvature, a preprint.
  4. L. E. Dubins, On curves of minimal length with a constraint on average curvature and with prescribed initial and terminal position and tangents, Amer. J. Math. 79 (1957), 497-516.
  5. V. Jurdjevic, Non-Euclidean elastica, Amer. J. Math. 117 (1995), 93-124.
  6. V. Jurdjevic, The geometry of the plate-ball problem, Arch. Rational Mech. Anal. 124 (1993), 305-328.
  7. V. Jurdjevic, Optimal Control Problems on Lie Groups: Crossroads between Geometry and Mechanics, in: The Geometry of Non-linear Feedback and Optimal Control, B. Jakubczyk and W. Respondek (eds.), Marcel Dekker, to appear.
  8. V. Jurdjevic and I. Kupka, Control systems on semi-simple Lie groups and their homogeneous spaces, Ann. Inst. Fourier (Grenoble) 31 (4) (1981), 151-179.
  9. C. Lobry, Controllability of non-linear systems on compact manifolds, SIAM J. Control 12 (1974), 1-4.
  10. J. P. Laumonde et P. Souriat, Synthèse des plus courts chemins pour la voiture de Reeds et Shepp, Repport LAAS/CNRS 92234, Juin 1992.
  11. J. A. Reeds and R. A. Shepp, Optimal paths for a car that goes both forward and backwards, Pacific J. Math. 145 (1990), 367-393.
  12. H. J. Sussmann and G. Tang, Shortest paths for the Reeds-Shepp car: A worked out example of the use of geometric techniques in non-linear optimal control, a preprint.
Banach Center Publications
1995/32/1
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Pages:
261-275
Main language of publication
English
Published
1995
Exact and natural sciences