Control to Facet for Polynomial Systems

Christoffer Sloth; Rafael Wisniewski

doi:10.1145/2562059.2562132

Control to Facet for Polynomial Systems

Publikation: Bidrag til bog/antologi/rapport/konference proceeding › Konferenceartikel i proceeding › Forskning › peer review

11 Citationer (Scopus)

Abstract

This paper presents a solution to the control to facet problem for arbitrary polynomial vector fields defined on simplices. The novelty of the work is to use Bernstein coefficients of polynomials for determining certificates of positivity. Specifically, the constraints that are set up for the controller design are solved by searching for polynomials in Bernstein form. This allows the controller design problem to be formulated as a linear programming problem. Examples are provided that demonstrate the efficiency of the method for designing controls for polynomial systems.

Originalsprog	Engelsk
Titel	Proceedings of the 17th ACM international conference on Hybrid Systems: Computation and Control
Forlag	Association for Computing Machinery
Publikationsdato	2014
Sider	123-132
ISBN (Trykt)	978-1-4503-2732-9
DOI	https://doi.org/10.1145/2562059.2562132
Status	Udgivet - 2014
Begivenhed	17th International Conference on Hybrid Systems: Computation and Control - Berlin, Tyskland Varighed: 15 apr. 2014 → 17 apr. 2014

Konference

Konference	17th International Conference on Hybrid Systems
Land/Område	Tyskland
By	Berlin
Periode	15/04/2014 → 17/04/2014

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10.1145/2562059.2562132

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Citationsformater

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title = "Control to Facet for Polynomial Systems",

abstract = "This paper presents a solution to the control to facet problem for arbitrary polynomial vector fields defined on simplices. The novelty of the work is to use Bernstein coefficients of polynomials for determining certificates of positivity. Specifically, the constraints that are set up for the controller design are solved by searching for polynomials in Bernstein form. This allows the controller design problem to be formulated as a linear programming problem. Examples are provided that demonstrate the efficiency of the method for designing controls for polynomial systems.",

author = "Christoffer Sloth and Rafael Wisniewski",

year = "2014",

doi = "10.1145/2562059.2562132",

language = "English",

isbn = "978-1-4503-2732-9",

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booktitle = "Proceedings of the 17th ACM international conference on Hybrid Systems: Computation and Control",

publisher = "Association for Computing Machinery",

address = "United States",

note = "17th International Conference on Hybrid Systems : Computation and Control , HSCC 2014 ; Conference date: 15-04-2014 Through 17-04-2014",

}

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T1 - Control to Facet for Polynomial Systems

AU - Sloth, Christoffer

AU - Wisniewski, Rafael

PY - 2014

Y1 - 2014

N2 - This paper presents a solution to the control to facet problem for arbitrary polynomial vector fields defined on simplices. The novelty of the work is to use Bernstein coefficients of polynomials for determining certificates of positivity. Specifically, the constraints that are set up for the controller design are solved by searching for polynomials in Bernstein form. This allows the controller design problem to be formulated as a linear programming problem. Examples are provided that demonstrate the efficiency of the method for designing controls for polynomial systems.

AB - This paper presents a solution to the control to facet problem for arbitrary polynomial vector fields defined on simplices. The novelty of the work is to use Bernstein coefficients of polynomials for determining certificates of positivity. Specifically, the constraints that are set up for the controller design are solved by searching for polynomials in Bernstein form. This allows the controller design problem to be formulated as a linear programming problem. Examples are provided that demonstrate the efficiency of the method for designing controls for polynomial systems.

U2 - 10.1145/2562059.2562132

DO - 10.1145/2562059.2562132

M3 - Article in proceeding

SN - 978-1-4503-2732-9

SP - 123

EP - 132

BT - Proceedings of the 17th ACM international conference on Hybrid Systems: Computation and Control

PB - Association for Computing Machinery

T2 - 17th International Conference on Hybrid Systems

Y2 - 15 April 2014 through 17 April 2014

ER -

Control to Facet for Polynomial Systems

Abstract

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