Variational approach to some optimization control problems

R. Bianchini

Banach Center Publications (1995)

  • Volume: 32, Issue: 1, page 83-94
  • ISSN: 0137-6934

Abstract

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This paper presents the variational approach to some optimization problems: Mayer's problem with or without constraints on the final point, local controllability of a trajectory, time-optimal problems.

How to cite

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Bianchini, R.. "Variational approach to some optimization control problems." Banach Center Publications 32.1 (1995): 83-94. <http://eudml.org/doc/262712>.

@article{Bianchini1995,
abstract = {This paper presents the variational approach to some optimization problems: Mayer's problem with or without constraints on the final point, local controllability of a trajectory, time-optimal problems.},
author = {Bianchini, R.},
journal = {Banach Center Publications},
keywords = {tangent vectors; variational cone; local controllability; Mayer's optimization problem; Meyer control problem; tangent cone; reference trajectory; necessary and sufficient conditions; Meyer optimization problem},
language = {eng},
number = {1},
pages = {83-94},
title = {Variational approach to some optimization control problems},
url = {http://eudml.org/doc/262712},
volume = {32},
year = {1995},
}

TY - JOUR
AU - Bianchini, R.
TI - Variational approach to some optimization control problems
JO - Banach Center Publications
PY - 1995
VL - 32
IS - 1
SP - 83
EP - 94
AB - This paper presents the variational approach to some optimization problems: Mayer's problem with or without constraints on the final point, local controllability of a trajectory, time-optimal problems.
LA - eng
KW - tangent vectors; variational cone; local controllability; Mayer's optimization problem; Meyer control problem; tangent cone; reference trajectory; necessary and sufficient conditions; Meyer optimization problem
UR - http://eudml.org/doc/262712
ER -

References

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  1. [1] M. S. Bazaraa and C. M. Shetty, Foundations of Optimization, Lecture Notes in Econom. and Math. Systems 122, Springer, Berlin, 1976. Zbl0334.90049
  2. [2] R. M. Bianchini and G. Stefani, Controllability along a reference trajectory: a variational approach, SIAM J. Control Optim. 31 (1993), 900-927. Zbl0797.49015
  3. [3] A. I. Dubovickiĭ and A. M. Miljutin, Extremum problems with constraints, J. Soviet Math. 4 (1963), 452-455. 
  4. [4] K. Grasse, Controllability and accessibility in nonlinear control systems, PhD thesis, University of Illinois at Urbana-Champaign, 1979. 
  5. [5] M. R. Hestenes, Calculus of Variations and Optimal Control Theory, Wiley, New York, 1966. 
  6. [6] E. B. Lee and L. Markus, Foundations of Optimal Control Theory, Wiley, New York, 1967. Zbl0159.13201
  7. [7] E. S. Polovinkin and G. V. Smirnov, An approach to the differentiation of many-valued mappings and necessary conditions for optimization of solutions of differential inclusions, Differencial'nye Uravnenija 22 (1986), 944-954. Zbl0604.49011
  8. [8] R. T. Rockafellar, Clarke’s tangent cones and the boundaries of closed convex sets in R n , Nonlinear Anal. 3 (1979), 145-154. 

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