Time minimal synthesis with target of codimension one under generic conditions

B. Bonnard; M. Pelletier

Banach Center Publications (1995)

  • Volume: 32, Issue: 1, page 95-109
  • ISSN: 0137-6934

Abstract

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We consider the problem of constructing the optimal closed loop control in the time minimal control problem, with terminal constraint belonging to a manifold of codimension one, for systems of the form v ̇ = X + u Y , | u | ≤ 1 and v ∈ R 2 or R 3 , under generic assumptions. The analysis is localized near the terminal manifold and is developed to control a class of chemical systems.

How to cite

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Bonnard, B., and Pelletier, M.. "Time minimal synthesis with target of codimension one under generic conditions." Banach Center Publications 32.1 (1995): 95-109. <http://eudml.org/doc/262776>.

@article{Bonnard1995,
abstract = {We consider the problem of constructing the optimal closed loop control in the time minimal control problem, with terminal constraint belonging to a manifold of codimension one, for systems of the form $v̇ = X + uY$, $|u| ≤ 1$ and $v ∈ R^2$ or $R^3$, under generic assumptions. The analysis is localized near the terminal manifold and is developed to control a class of chemical systems.},
author = {Bonnard, B., Pelletier, M.},
journal = {Banach Center Publications},
keywords = {time minimal synthesis; optimal closed loop control; time minimal control problem},
language = {eng},
number = {1},
pages = {95-109},
title = {Time minimal synthesis with target of codimension one under generic conditions},
url = {http://eudml.org/doc/262776},
volume = {32},
year = {1995},
}

TY - JOUR
AU - Bonnard, B.
AU - Pelletier, M.
TI - Time minimal synthesis with target of codimension one under generic conditions
JO - Banach Center Publications
PY - 1995
VL - 32
IS - 1
SP - 95
EP - 109
AB - We consider the problem of constructing the optimal closed loop control in the time minimal control problem, with terminal constraint belonging to a manifold of codimension one, for systems of the form $v̇ = X + uY$, $|u| ≤ 1$ and $v ∈ R^2$ or $R^3$, under generic assumptions. The analysis is localized near the terminal manifold and is developed to control a class of chemical systems.
LA - eng
KW - time minimal synthesis; optimal closed loop control; time minimal control problem
UR - http://eudml.org/doc/262776
ER -

References

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  1. [1] R. Benedetti and J. J. Risler, Real Algebraic and Semi-Algebraic Sets, Hermann, Paris, 1990. Zbl0694.14006
  2. [2] B. Bonnard et 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. 
  3. [3] B. Bonnard and J. de Morant, Towards a geometric theory in the time minimal control of chemical batch reactors, to appear in SIAM J. Control Optim. Zbl0882.49024
  4. [4] B. Bonnard and M. Pelletier, Time minimal synthesis for planar systems in the neighborhood of a terminal manifold of codimension one, preprint, Laboratoire de Topologie de Dijon, 1992, to appear in JMSEC. 
  5. [5] I. Kupka, Geometric theory of extremals in optimal control problems. I. The fold and Maxwell cases, Trans. Amer. Math. Soc. 299 (1977), 225-243. Zbl0606.49016
  6. [6] E. B. Lee and L. Markus, Foundations of Optimal Control Theory, Wiley, New York, 1967. Zbl0159.13201
  7. [7] H. Poincaré, Sur les lignes géodésiques des surfaces convexes, Trans. Amer. Math. Soc. 6 (1905), 237-274. Zbl36.0669.01
  8. [8] H. Schättler, The local structure of time optimal trajectories under generic conditions, SIAM J. Control Optim. 26 (1988), 899-918. Zbl0656.49007
  9. [9] H. J. Sussmann, The structure of time optimal trajectories for single-input systems in the plane: the C ∞ non singular case, ibid. 25 (1987), 433-465. 
  10. [10] H. J. Sussmann, Regular synthesis for time optimal control single-input real analytic systems in the plane, ibid. 25 (1987), 1145-1162. Zbl0701.93035

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