The Barycentric Bernstein Form for Control Design

Tareq Hamadneh; Rafal Wisniewski

doi:10.23919/ACC.2018.8431599

The Barycentric Bernstein Form for Control Design

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

7 Citationer (Scopus)

Abstract

In this paper, an algorithm for computing a polynomial control and a polynomial Lyapunov function in the simplicial Bernstein form is developed. This ensures asymptotic stability of the designed feedback system. To this end, we provide certificates of positivity for polynomials in the simplicial Bernstein form. Subsequently, the state space is partitioned into simplices. On each simplex, we simultaneously compute Lyapunov and control functions. With this control, the equilibrium is asymptotically stable.

Originalsprog	Engelsk
Titel	2018 Annual American Control Conference (ACC)
Antal sider	6
Forlag	IEEE
Publikationsdato	16 aug. 2018
Sider	3738-3743
Artikelnummer	8431599
ISBN (Trykt)	978-1-5386-5429-3
ISBN (Elektronisk)	978-1-5386-5428-6
DOI	https://doi.org/10.23919/ACC.2018.8431599
Status	Udgivet - 16 aug. 2018
Begivenhed	2018 American Control Conference: 2018 American Control Conference - Wisconsin Center, Milwaukee, USA Varighed: 27 jun. 2018 → 29 jun. 2018 http://acc2018.a2c2.org/ http://acc2018.a2c2.org/

Konference

Konference	2018 American Control Conference
Lokation	Wisconsin Center
Land/Område	USA
By	Milwaukee
Periode	27/06/2018 → 29/06/2018
Internetadresse	http://acc2018.a2c2.org/ http://acc2018.a2c2.org/

Adgang til dokumentet

10.23919/ACC.2018.8431599

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Citationsformater

@inproceedings{d94fc9d06b024437b253d139800941dd,

title = "The Barycentric Bernstein Form for Control Design",

abstract = "In this paper, an algorithm for computing a polynomial control and a polynomial Lyapunov function in the simplicial Bernstein form is developed. This ensures asymptotic stability of the designed feedback system. To this end, we provide certificates of positivity for polynomials in the simplicial Bernstein form. Subsequently, the state space is partitioned into simplices. On each simplex, we simultaneously compute Lyapunov and control functions. With this control, the equilibrium is asymptotically stable.",

keywords = "Bernstein polynomial, certificates of positivity, control design, inclusion isotonicity, stability",

author = "Tareq Hamadneh and Rafal Wisniewski",

year = "2018",

month = aug,

day = "16",

doi = "10.23919/ACC.2018.8431599",

language = "English",

isbn = "978-1-5386-5429-3",

pages = "3738--3743",

booktitle = "2018 Annual American Control Conference (ACC)",

publisher = "IEEE",

address = "United States",

note = "2018 American Control Conference : 2018 American Control Conference, ACC ; Conference date: 27-06-2018 Through 29-06-2018",

url = "http://acc2018.a2c2.org/, http://acc2018.a2c2.org/",

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T1 - The Barycentric Bernstein Form for Control Design

AU - Hamadneh, Tareq

AU - Wisniewski, Rafal

PY - 2018/8/16

Y1 - 2018/8/16

N2 - In this paper, an algorithm for computing a polynomial control and a polynomial Lyapunov function in the simplicial Bernstein form is developed. This ensures asymptotic stability of the designed feedback system. To this end, we provide certificates of positivity for polynomials in the simplicial Bernstein form. Subsequently, the state space is partitioned into simplices. On each simplex, we simultaneously compute Lyapunov and control functions. With this control, the equilibrium is asymptotically stable.

AB - In this paper, an algorithm for computing a polynomial control and a polynomial Lyapunov function in the simplicial Bernstein form is developed. This ensures asymptotic stability of the designed feedback system. To this end, we provide certificates of positivity for polynomials in the simplicial Bernstein form. Subsequently, the state space is partitioned into simplices. On each simplex, we simultaneously compute Lyapunov and control functions. With this control, the equilibrium is asymptotically stable.

KW - Bernstein polynomial

KW - certificates of positivity

KW - control design

KW - inclusion isotonicity

KW - stability

UR - http://www.scopus.com/inward/record.url?scp=85052603440&partnerID=8YFLogxK

U2 - 10.23919/ACC.2018.8431599

DO - 10.23919/ACC.2018.8431599

M3 - Article in proceeding

SN - 978-1-5386-5429-3

SP - 3738

EP - 3743

BT - 2018 Annual American Control Conference (ACC)

PB - IEEE

T2 - 2018 American Control Conference

Y2 - 27 June 2018 through 29 June 2018

ER -