Control to Facet for Polynomial Systems

Christoffer Sloth; Rafael Wisniewski

doi:10.1145/2562059.2562132

Control to Facet for Polynomial Systems

Research output: Contribution to book/anthology/report/conference proceeding › Article in proceeding › Research › peer-review

11 Citations (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.

Original language	English
Title of host publication	Proceedings of the 17th ACM international conference on Hybrid Systems: Computation and Control
Publisher	Association for Computing Machinery
Publication date	2014
Pages	123-132
ISBN (Print)	978-1-4503-2732-9
DOIs	https://doi.org/10.1145/2562059.2562132
Publication status	Published - 2014
Event	17th International Conference on Hybrid Systems: Computation and Control - Berlin, Germany Duration: 15 Apr 2014 → 17 Apr 2014

Conference

Conference	17th International Conference on Hybrid Systems
Country/Territory	Germany
City	Berlin
Period	15/04/2014 → 17/04/2014

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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",

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language = "English",

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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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AU - Wisniewski, Rafael

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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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