Control design and Lyapunov Functions via Bernstein Approximations: Exact Results

Tareq Hamadneh; Nikolaos Athanasopoulos; Rafael Wisniewski

doi:10.1016/j.ifacol.2020.12.1789

Control design and Lyapunov Functions via Bernstein Approximations: Exact Results

Tareq Hamadneh, Nikolaos Athanasopoulos, Rafael Wisniewski

School of Electronics, Electrical Engineering and Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

4 Citations (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.

Original language	English
Title of host publication	IFAC World Congress
Publisher	Elsevier
Pages	6459-6464
Number of pages	6
Volume	53
Edition	2
DOIs	https://doi.org/10.1016/j.ifacol.2020.12.1789
Publication status	Published - 14 Apr 2020

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Control design and Lyapunov Functions via Bernstein Approximations: Exact Results
© 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. This manuscript is distributed under a Creative Commons Attribution-NonCommercial-NoDerivs License (https://creativecommons.org/licenses/by-nc-nd/4.0/), which permits distribution and reproduction for non-commercial purposes, provided the author and source are cited.
Accepted author manuscript, 227 KBLicence: CC BY-NC-ND

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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.",

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AU - Hamadneh, Tareq

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AU - Wisniewski, Rafael

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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.

U2 - 10.1016/j.ifacol.2020.12.1789

DO - 10.1016/j.ifacol.2020.12.1789

M3 - Conference contribution

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EP - 6464

BT - IFAC World Congress

PB - Elsevier

ER -

Control design and Lyapunov Functions via Bernstein Approximations: Exact Results

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