Casimir elements and optimal control

V. Jurdjevic

Banach Center Publications (1995)

  • Volume: 32, Issue: 1, page 261-275
  • ISSN: 0137-6934

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Jurdjevic, V.. "Casimir elements and optimal control." Banach Center Publications 32.1 (1995): 261-275. <http://eudml.org/doc/262645>.

@article{Jurdjevic1995,
author = {Jurdjevic, V.},
journal = {Banach Center Publications},
keywords = {maximum principle; time optimal control problems on Lie groups; Casimir elements},
language = {eng},
number = {1},
pages = {261-275},
title = {Casimir elements and optimal control},
url = {http://eudml.org/doc/262645},
volume = {32},
year = {1995},
}

TY - JOUR
AU - Jurdjevic, V.
TI - Casimir elements and optimal control
JO - Banach Center Publications
PY - 1995
VL - 32
IS - 1
SP - 261
EP - 275
LA - eng
KW - maximum principle; time optimal control problems on Lie groups; Casimir elements
UR - http://eudml.org/doc/262645
ER -

References

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  1. [1] V. I. Arnold, Méthodes Mathématiques de la Mécanique Classique, Editions Mir, 1976. 
  2. [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. Zbl0519.49023
  3. [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. [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. Zbl0098.35401
  5. [5] V. Jurdjevic, Non-Euclidean elastica, Amer. J. Math. 117 (1995), 93-124. 
  6. [6] V. Jurdjevic, The geometry of the plate-ball problem, Arch. Rational Mech. Anal. 124 (1993), 305-328. Zbl0809.70005
  7. [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. [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. Zbl0453.93011
  9. [9] C. Lobry, Controllability of non-linear systems on compact manifolds, SIAM J. Control 12 (1974), 1-4. Zbl0286.93006
  10. [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. [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. [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. 

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