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

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

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

Mathematics

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

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. © 2003 Elsevier Ltd. All rights reserved.

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

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habets:schuppen:2004

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10.1016/j.automatica.2003.08.001

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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. © 2003 Elsevier Ltd. All rights reserved.

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

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