Viability Kernels and Control Sets

Dietmar Szolnoki

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 5, page 175-185
  • ISSN: 1292-8119

Abstract

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This paper analyzes the relation of viability kernels and control sets of control affine systems. A viability kernel describes the largest closed viability domain contained in some closed subset Q of the state space. On the other hand, control sets are maximal regions of the state space where approximate controllability holds. It turns out that the viability kernel of Q can be represented by the union of domains of attraction of chain control sets, defined relative to the given set Q. In particular, with this result control sets and their domains of attraction can be computed using techniques for the computation of attractors and viability kernels.

How to cite

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Szolnoki, Dietmar. "Viability Kernels and Control Sets." ESAIM: Control, Optimisation and Calculus of Variations 5 (2010): 175-185. <http://eudml.org/doc/197374>.

@article{Szolnoki2010,
abstract = { This paper analyzes the relation of viability kernels and control sets of control affine systems. A viability kernel describes the largest closed viability domain contained in some closed subset Q of the state space. On the other hand, control sets are maximal regions of the state space where approximate controllability holds. It turns out that the viability kernel of Q can be represented by the union of domains of attraction of chain control sets, defined relative to the given set Q. In particular, with this result control sets and their domains of attraction can be computed using techniques for the computation of attractors and viability kernels. },
author = {Szolnoki, Dietmar},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Control affine system; viability kernel; reachable set; control set; chain control set; control flow.; control affine system; control flow; viability kernels},
language = {eng},
month = {3},
pages = {175-185},
publisher = {EDP Sciences},
title = {Viability Kernels and Control Sets},
url = {http://eudml.org/doc/197374},
volume = {5},
year = {2010},
}

TY - JOUR
AU - Szolnoki, Dietmar
TI - Viability Kernels and Control Sets
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 5
SP - 175
EP - 185
AB - This paper analyzes the relation of viability kernels and control sets of control affine systems. A viability kernel describes the largest closed viability domain contained in some closed subset Q of the state space. On the other hand, control sets are maximal regions of the state space where approximate controllability holds. It turns out that the viability kernel of Q can be represented by the union of domains of attraction of chain control sets, defined relative to the given set Q. In particular, with this result control sets and their domains of attraction can be computed using techniques for the computation of attractors and viability kernels.
LA - eng
KW - Control affine system; viability kernel; reachable set; control set; chain control set; control flow.; control affine system; control flow; viability kernels
UR - http://eudml.org/doc/197374
ER -

References

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  7. W. KLIEMANN, Qualitative Theorie Nichtlinearer Stochastischer Systeme. Dissertation, Universität Bremen (1980).  
  8. H. NIJMEIJER AND A.J. VAN DER SCHAFT, Nonlinear Dynamical Control Systems. Springer-Verlag (1990).  Zbl0701.93001
  9. P. SAINT-PIERRE, Approximation of the viability kernel. Appl. Math. Optim.29 (1994) 187-209.  Zbl0790.65081
  10. height 2pt depth -1.6pt width 23pt, Set-valued numerical analysis for optimal control and differential games (1998) to appear.  
  11. D. SZOLNOKI, Berechnung von Viabilitätskernen. Diplomarbeit, Institut für Mathematik, Universität Augsburg, Augsburg (1997).  
  12. A. UPPAL, W.H. RAY AND A.B. POORE, On the dynamic behavior of continuous stirred tank reactors. Chem. Engrg. Sci.19 (1974) 967-985.  

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