Control design and Lyapunov Functions via Bernstein Approximations: Exact Results

Tareq Hamadneh; Nikolaos Athanasopoulos; Rafal Wisniewski

doi:10.1016/j.ifacol.2020.12.1789

Control design and Lyapunov Functions via Bernstein Approximations: Exact Results

Tareq Hamadneh, Nikolaos Athanasopoulos, Rafal Wisniewski

Publikation: Bidrag til tidsskrift › Konferenceartikel i tidsskrift › Forskning › peer review

4 Citationer (Scopus)

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Abstract

We study the control problem for polynomial continuous-time dynamical systems. We consider polynomial Lyapunov functions and controllers, both parameterised in Bernstein form. Specifically, we present necessary and sufficient conditions for existence of polynomial controllers and Lyapunov functions of some maximum degree, providing at the same time explicit upper bounds on the degree of the involved Bernstein polynomials. The formulated conditions are a set of algebraic inequalities, in the space of Bernstein coefficients.

Originalsprog	Engelsk
Bogserie	IFAC-PapersOnLine
Vol/bind	53
Udgave nummer	2
Sider (fra-til)	6459-6464
Antal sider	6
ISSN	2405-8963
DOI	https://doi.org/10.1016/j.ifacol.2020.12.1789
Status	Udgivet - 2020
Begivenhed	21th IFAC World Congress - Berlin, Tyskland Varighed: 12 jul. 2020 → 17 jul. 2020

Konference

Konference	21th IFAC World Congress
Land/Område	Tyskland
By	Berlin
Periode	12/07/2020 → 17/07/2020

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10.1016/j.ifacol.2020.12.1789

Control design and Lyapunov Functions via Bernstein ApproximationsForlagets udgivne version, 365 KBLicens: CC BY-NC-ND 4.0

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title = "Control design and Lyapunov Functions via Bernstein Approximations: Exact Results",

abstract = "We study the control problem for polynomial continuous-time dynamical systems. We consider polynomial Lyapunov functions and controllers, both parameterised in Bernstein form. Specifically, we present necessary and sufficient conditions for existence of polynomial controllers and Lyapunov functions of some maximum degree, providing at the same time explicit upper bounds on the degree of the involved Bernstein polynomials. The formulated conditions are a set of algebraic inequalities, in the space of Bernstein coefficients.",

keywords = "Bernstein polynomials, Certificates of positivity, Control design, Control lyapunov functions, Lyapunov stability, Polynomial systems",

author = "Tareq Hamadneh and Nikolaos Athanasopoulos and Rafal Wisniewski",

year = "2020",

doi = "10.1016/j.ifacol.2020.12.1789",

language = "English",

volume = "53",

pages = "6459--6464",

journal = "IFAC-PapersOnLine",

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note = "21th IFAC World Congress ; Conference date: 12-07-2020 Through 17-07-2020",

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T2 - 21th IFAC World Congress

AU - Hamadneh, Tareq

AU - Athanasopoulos, Nikolaos

AU - Wisniewski, Rafal

PY - 2020

Y1 - 2020

N2 - We study the control problem for polynomial continuous-time dynamical systems. We consider polynomial Lyapunov functions and controllers, both parameterised in Bernstein form. Specifically, we present necessary and sufficient conditions for existence of polynomial controllers and Lyapunov functions of some maximum degree, providing at the same time explicit upper bounds on the degree of the involved Bernstein polynomials. The formulated conditions are a set of algebraic inequalities, in the space of Bernstein coefficients.

AB - We study the control problem for polynomial continuous-time dynamical systems. We consider polynomial Lyapunov functions and controllers, both parameterised in Bernstein form. Specifically, we present necessary and sufficient conditions for existence of polynomial controllers and Lyapunov functions of some maximum degree, providing at the same time explicit upper bounds on the degree of the involved Bernstein polynomials. The formulated conditions are a set of algebraic inequalities, in the space of Bernstein coefficients.

KW - Bernstein polynomials

KW - Certificates of positivity

KW - Control design

KW - Control lyapunov functions

KW - Lyapunov stability

KW - Polynomial systems

UR - http://www.scopus.com/inward/record.url?scp=85105113522&partnerID=8YFLogxK

U2 - 10.1016/j.ifacol.2020.12.1789

DO - 10.1016/j.ifacol.2020.12.1789

M3 - Conference article in Journal

SN - 2405-8963

VL - 53

SP - 6459

EP - 6464

JO - IFAC-PapersOnLine

JF - IFAC-PapersOnLine

IS - 2

Y2 - 12 July 2020 through 17 July 2020

ER -

Control design and Lyapunov Functions via Bernstein Approximations: Exact Results

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