Well-posedness and sliding mode control

Tullio Zolezzi

ESAIM: Control, Optimisation and Calculus of Variations (2005)

  • 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 (2005): 219-228. <http://eudml.org/doc/245048>.

@article{Zolezzi2005,
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; Sliding mode control},
language = {eng},
number = {2},
pages = {219-228},
publisher = {EDP-Sciences},
title = {Well-posedness and sliding mode control},
url = {http://eudml.org/doc/245048},
volume = {11},
year = {2005},
}

TY - JOUR
AU - Zolezzi, Tullio
TI - Well-posedness and sliding mode control
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2005
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; Sliding mode control
UR - http://eudml.org/doc/245048
ER -

References

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  8. [8] A. Dontchev and T. Zolezzi, Well-posed optimization problems, Springer. Lect. Notes Math. 1543 (1993). Zbl0797.49001MR1239439
  9. [9] C. Edwards and S. Spurgeon, Sliding mode control: theory and applications. Taylor and Francis (1988). 
  10. [10] A.F. Filippov, Differential equations with discontinuous right-hand side. Amer. Math. Soc. Transl. 42 (1964) 199–231. Zbl0148.33002
  11. [11] A.F. Filippov, Differential equations with discontinuous righthand sides. Kluwer (1988). Zbl0664.34001MR1028776
  12. [12] W. Perruquetti and J.P. Barbot Eds., Sliding mode control in engineering. Dekker (2002). 
  13. [13] R.T. Rockafellar, Integral functionals, normal integrands and measurable selections, Springer. Lect. Notes Math. 543 (1976) 157–207. Zbl0374.49001
  14. [14] V. Utkin, Sliding modes in control and optimization. Springer (1992). Zbl0748.93044MR1295845

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