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

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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

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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.",

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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.

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DO - 10.1016/j.automatica.2003.08.001

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JO - Automatica

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

Abstract

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