Well-posedness and sliding mode control

Tullio Zolezzi

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

  • Volume: 11, Issue: 2, page 219-228
  • ISSN: 1292-8119

Abstract

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Sliding mode control of ordinary differential equations is considered. A key robustness property, called approximability, is studied from an optimization point of view. It is proved that Tikhonov well-posedness of a suitably defined optimization problem is intimately related to approximability. Making use of this link, new approximability criteria are obtained for nonlinear sliding mode control systems.

How to cite

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Zolezzi, Tullio. "Well-posedness and sliding mode control." ESAIM: Control, Optimisation and Calculus of Variations 11.2 (2010): 219-228. <http://eudml.org/doc/90762>.

@article{Zolezzi2010,
abstract = { Sliding mode control of ordinary differential equations is considered. A key robustness property, called approximability, is studied from an optimization point of view. It is proved that Tikhonov well-posedness of a suitably defined optimization problem is intimately related to approximability. Making use of this link, new approximability criteria are obtained for nonlinear sliding mode control systems. },
author = {Zolezzi, Tullio},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Sliding mode control; Tikhonov well-posedness; approximability.; approximability},
language = {eng},
month = {3},
number = {2},
pages = {219-228},
publisher = {EDP Sciences},
title = {Well-posedness and sliding mode control},
url = {http://eudml.org/doc/90762},
volume = {11},
year = {2010},
}

TY - JOUR
AU - Zolezzi, Tullio
TI - Well-posedness and sliding mode control
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 11
IS - 2
SP - 219
EP - 228
AB - Sliding mode control of ordinary differential equations is considered. A key robustness property, called approximability, is studied from an optimization point of view. It is proved that Tikhonov well-posedness of a suitably defined optimization problem is intimately related to approximability. Making use of this link, new approximability criteria are obtained for nonlinear sliding mode control systems.
LA - eng
KW - Sliding mode control; Tikhonov well-posedness; approximability.; approximability
UR - http://eudml.org/doc/90762
ER -

References

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  8. A. Dontchev and T. Zolezzi, Well-posed optimization problems, Springer. Lect. Notes Math.1543 (1993).  Zbl0797.49001
  9. C. Edwards and S. Spurgeon, Sliding mode control: theory and applications. Taylor and Francis (1988).  
  10. A.F. Filippov, Differential equations with discontinuous right-hand side. Amer. Math. Soc. Transl.42 (1964) 199–231.  Zbl0148.33002
  11. A.F. Filippov, Differential equations with discontinuous righthand sides. Kluwer (1988).  
  12. W. Perruquetti and J.P. Barbot Eds., Sliding mode control in engineering. Dekker (2002).  
  13. R.T. Rockafellar, Integral functionals, normal integrands and measurable selections, Springer. Lect. Notes Math.543 (1976) 157–207.  Zbl0374.49001
  14. V. Utkin, Sliding modes in control and optimization. Springer (1992).  Zbl0748.93044

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