Patchy Vector Fields and Asymptotic Stabilization

Fabio Ancona; Alberto Bressan

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

  • Volume: 4, page 445-471
  • ISSN: 1292-8119

Abstract

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This paper is concerned with the structure of asymptotically stabilizing feedbacks for a nonlinear control system on n . We first introduce a family of discontinuous, piecewise smooth vector fields and derive a number of properties enjoyed by solutions of the corresponding O.D.E's. We then define a class of “patchy feedbacks” which are obtained by patching together a locally finite family of smooth controls. Our main result shows that, if a system is asymptotically controllable at the origin, then it can be stabilized by a piecewise constant patchy feedback control.

How to cite

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Ancona, Fabio, and Bressan, Alberto. "Patchy Vector Fields and Asymptotic Stabilization." ESAIM: Control, Optimisation and Calculus of Variations 4 (2010): 445-471. <http://eudml.org/doc/116552>.

@article{Ancona2010,
abstract = { This paper is concerned with the structure of asymptotically stabilizing feedbacks for a nonlinear control system on $\mathbb\{R\}^n$. We first introduce a family of discontinuous, piecewise smooth vector fields and derive a number of properties enjoyed by solutions of the corresponding O.D.E's. We then define a class of “patchy feedbacks” which are obtained by patching together a locally finite family of smooth controls. Our main result shows that, if a system is asymptotically controllable at the origin, then it can be stabilized by a piecewise constant patchy feedback control. },
author = {Ancona, Fabio, Bressan, Alberto},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = { Asymptotic controllability; feedback asymptotic stabilization; discontinuous feedback; discontinuous vector fields. ; asymptotic controllability; feedback asymptotic stabilization; discontinuous feedback; discontinuous vector fields},
language = {eng},
month = {3},
pages = {445-471},
publisher = {EDP Sciences},
title = {Patchy Vector Fields and Asymptotic Stabilization},
url = {http://eudml.org/doc/116552},
volume = {4},
year = {2010},
}

TY - JOUR
AU - Ancona, Fabio
AU - Bressan, Alberto
TI - Patchy Vector Fields and Asymptotic Stabilization
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 4
SP - 445
EP - 471
AB - This paper is concerned with the structure of asymptotically stabilizing feedbacks for a nonlinear control system on $\mathbb{R}^n$. We first introduce a family of discontinuous, piecewise smooth vector fields and derive a number of properties enjoyed by solutions of the corresponding O.D.E's. We then define a class of “patchy feedbacks” which are obtained by patching together a locally finite family of smooth controls. Our main result shows that, if a system is asymptotically controllable at the origin, then it can be stabilized by a piecewise constant patchy feedback control.
LA - eng
KW - Asymptotic controllability; feedback asymptotic stabilization; discontinuous feedback; discontinuous vector fields. ; asymptotic controllability; feedback asymptotic stabilization; discontinuous feedback; discontinuous vector fields
UR - http://eudml.org/doc/116552
ER -

References

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