A control problem for affine dynamical systems on a full-dimensional polytope

L.C.G.J.M. Habets; J.H. Schuppen, van

doi:10.1016/j.automatica.2003.08.001

A control problem for affine dynamical systems on a full-dimensional polytope

L.C.G.J.M. Habets, J.H. Schuppen, van

Center for Analysis, Scientific Computing and Applications

Research output: Contribution to journal › Article › Academic › peer-review

167 Citations (Scopus)

5 Downloads (Pure)

Abstract

Given an affine system on a full-dimensional polytope, the problem of reaching a particular facet of the polytope, using continuous piecewise-affine state feedback is studied. Necessary conditions and sufficient conditions for the existence of a solution are derived in terms of linear inequalities on the input vectors at the vertices of the polytope. Special attention is paid to affine systems on full-dimensional simplices. In this case, the necessary and sufficient conditions are equivalent and a constructive procedure yields an affine feedback control law, that solves the reachability problem under consideration.

Original language	English
Pages (from-to)	21-35
Journal	Automatica
Volume	40
Issue number	1
DOIs	https://doi.org/10.1016/j.automatica.2003.08.001
Publication status	Published - 2004

Access to Document

10.1016/j.automatica.2003.08.001

Cite this

@article{b34e74d8305241b0b0df7e91abe84b8b,

title = "A control problem for affine dynamical systems on a full-dimensional polytope",

abstract = "Given an affine system on a full-dimensional polytope, the problem of reaching a particular facet of the polytope, using continuous piecewise-affine state feedback is studied. Necessary conditions and sufficient conditions for the existence of a solution are derived in terms of linear inequalities on the input vectors at the vertices of the polytope. Special attention is paid to affine systems on full-dimensional simplices. In this case, the necessary and sufficient conditions are equivalent and a constructive procedure yields an affine feedback control law, that solves the reachability problem under consideration.",

author = "L.C.G.J.M. Habets and {Schuppen, van}, J.H.",

year = "2004",

doi = "10.1016/j.automatica.2003.08.001",

language = "English",

volume = "40",

pages = "21--35",

journal = "Automatica",

issn = "0005-1098",

publisher = "Elsevier",

number = "1",

}

TY - JOUR

T1 - A control problem for affine dynamical systems on a full-dimensional polytope

AU - Habets, L.C.G.J.M.

AU - Schuppen, van, J.H.

PY - 2004

Y1 - 2004

N2 - Given an affine system on a full-dimensional polytope, the problem of reaching a particular facet of the polytope, using continuous piecewise-affine state feedback is studied. Necessary conditions and sufficient conditions for the existence of a solution are derived in terms of linear inequalities on the input vectors at the vertices of the polytope. Special attention is paid to affine systems on full-dimensional simplices. In this case, the necessary and sufficient conditions are equivalent and a constructive procedure yields an affine feedback control law, that solves the reachability problem under consideration.

AB - Given an affine system on a full-dimensional polytope, the problem of reaching a particular facet of the polytope, using continuous piecewise-affine state feedback is studied. Necessary conditions and sufficient conditions for the existence of a solution are derived in terms of linear inequalities on the input vectors at the vertices of the polytope. Special attention is paid to affine systems on full-dimensional simplices. In this case, the necessary and sufficient conditions are equivalent and a constructive procedure yields an affine feedback control law, that solves the reachability problem under consideration.

U2 - 10.1016/j.automatica.2003.08.001

DO - 10.1016/j.automatica.2003.08.001

M3 - Article

SN - 0005-1098

VL - 40

SP - 21

EP - 35

JO - Automatica

JF - Automatica

IS - 1

ER -

A control problem for affine dynamical systems on a full-dimensional polytope

Abstract

Access to Document

Fingerprint

Cite this