Symmetries and integrals of motion in optimal control

H. Sussmann

Banach Center Publications (1995)

  • Volume: 32, Issue: 1, page 379-393
  • ISSN: 0137-6934

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Sussmann, H.. "Symmetries and integrals of motion in optimal control." Banach Center Publications 32.1 (1995): 379-393. <http://eudml.org/doc/262687>.

@article{Sussmann1995,
author = {Sussmann, H.},
journal = {Banach Center Publications},
keywords = {integrals of optimal solutions; hamiltonian methods},
language = {eng},
number = {1},
pages = {379-393},
title = {Symmetries and integrals of motion in optimal control},
url = {http://eudml.org/doc/262687},
volume = {32},
year = {1995},
}

TY - JOUR
AU - Sussmann, H.
TI - Symmetries and integrals of motion in optimal control
JO - Banach Center Publications
PY - 1995
VL - 32
IS - 1
SP - 379
EP - 393
LA - eng
KW - integrals of optimal solutions; hamiltonian methods
UR - http://eudml.org/doc/262687
ER -

References

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  1. [1] F. Albrecht, Topics in Control Theory, Springer, Berlin, 1968. Zbl0165.10604
  2. [2] L. D. Berkovitz, Optimal Control Theory, Springer, New York, 1974. Zbl0295.49001
  3. [3] F. H. Clarke, Optimization and Nonsmooth Analysis, Wiley Interscience, New York, 1983. Zbl0582.49001
  4. [4] L. E. Dubins, On curves of minimal length with a constraint on average curvature and with prescribed initial and terminal positions and tangents, Amer. J. Math. 79 (1957), 497-516. Zbl0098.35401
  5. [5] B. Kaskosz and S. Łojasiewicz Jr., A Maximum Principle for generalized control systems, Nonlinear Anal. 9 (1985), 109-130. Zbl0557.49012
  6. [6] E. B. Lee and L. Markus, Foundations of Optimal Control Theory, Wiley, New York, 1967. Zbl0159.13201
  7. [7] A. A. Markov, Some examples of the solution of a special kind of problem in greatest and least quantities, Soobshch. Kharkovsk. Mat. Obshch. 1 (1887), 250-276 (in Russian). 
  8. [8] L. S. Pontryagin, V. G. Boltyanskiĭ, R. V. Gamkrelidze and E. F. Mishchenko, The Mathematical Theory of Optimal Processes, (translated by K. N. Trigoroff, L. W. Neustadt, editor), Wiley, 1962. 
  9. [9] J. A. Reeds and L. A. Shepp, Optimal paths for a car that goes both forwards and backwards, Pacific J. Math. 145 (1990), 367-393. 
  10. [10] H. J. Sussmann, Orbits of families of vector fields and integrability of distributions, Trans. Amer. Math. Soc. 180 (1973), 171-188. Zbl0274.58002
  11. [11] H. J. Sussmann and G. Tang, Shortest paths for the Reeds-Shepp car: a worked out example of the use of geometric techniques in nonlinear optimal control, SIAM J. Control, to appear. 
  12. [12] H. J. Sussmann, Shortest paths with a prescribed bound on the curvature: the three-dimensional case, in preparation. 
  13. [13] H. J. Sussmann, An introduction to the coordinate-free Maximum Principle, in preparation. Zbl0925.93135

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