Combinatorial Vector Fields for Piecewise Affine Control Systems

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5 Citations (Scopus)

Abstract

This paper is intended to be a continuation of Habets and van Schuppen (2004) and Habets, Collins and van Schuppen (2006), which address the control problem for piecewise-affine systems on an arbitrary polytope or a family of these. Our work deals with the underlying combinatorics of the underlying discrete system. Motivated by Forman (1998), on the triangulated state space we define a combinatorial vector field, which indicates for a given face the future simplex. In the suggested definition we allow nondeterminacy in form of splitting and merging of solution trajectories. The combinatorial vector field gives rise to combinatorial counterparts of the flow lines. The main result is then an algorithm for synthesis of supervisory control.
Original languageEnglish
Book seriesElsevier IFAC Publications / IFAC Proceedings series
Issue number1
Number of pages6
ISSN1474-6670
Publication statusPublished - 2008
Event17th IFAC World Congress - Seoul, Korea, Republic of
Duration: 6 Jul 200811 Jul 2008
Conference number: 17

Conference

Conference17th IFAC World Congress
Number17
CountryKorea, Republic of
CitySeoul
Period06/07/200811/07/2008

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Control systems
Merging
Trajectories

Cite this

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title = "Combinatorial Vector Fields for Piecewise Affine Control Systems",
abstract = "This paper is intended to be a continuation of Habets and van Schuppen (2004) and Habets, Collins and van Schuppen (2006), which address the control problem for piecewise-affine systems on an arbitrary polytope or a family of these. Our work deals with the underlying combinatorics of the underlying discrete system. Motivated by Forman (1998), on the triangulated state space we define a combinatorial vector field, which indicates for a given face the future simplex. In the suggested definition we allow nondeterminacy in form of splitting and merging of solution trajectories. The combinatorial vector field gives rise to combinatorial counterparts of the flow lines. The main result is then an algorithm for synthesis of supervisory control.",
author = "Rafal Wisniewski and Larsen, {Jesper Abildgaard}",
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Combinatorial Vector Fields for Piecewise Affine Control Systems. / Wisniewski, Rafal; Larsen, Jesper Abildgaard.

In: Elsevier IFAC Publications / IFAC Proceedings series, No. 1, 2008.

Research output: Contribution to journalConference article in JournalResearchpeer-review

TY - GEN

T1 - Combinatorial Vector Fields for Piecewise Affine Control Systems

AU - Wisniewski, Rafal

AU - Larsen, Jesper Abildgaard

N1 - Volumne: 17

PY - 2008

Y1 - 2008

N2 - This paper is intended to be a continuation of Habets and van Schuppen (2004) and Habets, Collins and van Schuppen (2006), which address the control problem for piecewise-affine systems on an arbitrary polytope or a family of these. Our work deals with the underlying combinatorics of the underlying discrete system. Motivated by Forman (1998), on the triangulated state space we define a combinatorial vector field, which indicates for a given face the future simplex. In the suggested definition we allow nondeterminacy in form of splitting and merging of solution trajectories. The combinatorial vector field gives rise to combinatorial counterparts of the flow lines. The main result is then an algorithm for synthesis of supervisory control.

AB - This paper is intended to be a continuation of Habets and van Schuppen (2004) and Habets, Collins and van Schuppen (2006), which address the control problem for piecewise-affine systems on an arbitrary polytope or a family of these. Our work deals with the underlying combinatorics of the underlying discrete system. Motivated by Forman (1998), on the triangulated state space we define a combinatorial vector field, which indicates for a given face the future simplex. In the suggested definition we allow nondeterminacy in form of splitting and merging of solution trajectories. The combinatorial vector field gives rise to combinatorial counterparts of the flow lines. The main result is then an algorithm for synthesis of supervisory control.

M3 - Conference article in Journal

JO - I F A C Workshop Series

JF - I F A C Workshop Series

SN - 1474-6670

IS - 1

ER -