Algorithm for Bernstein Polynomial Control Design

Tareq Hamadneh, Rafael Wisniewski

Research output: Contribution to conference without publisher/journalConference abstract for conferenceResearchpeer-review

Abstract

This paper considers control synthesis for polynomial control systems. The developed method leans upon Lyapunov stability and Bernstein certificates of positivity. We strive to develop an algorithm that computes a polynomial control and a polynomial Lyaponov function in the simplicial Bernstein form. Subsequently, we reduce the control synthesis problem to a finite number of evaluations of a polynomial within Bernstein coefficient bounds representing controls and Lyapunov functions. As a consequence, the equilibrium is asymptotically stable with this control.
Original languageEnglish
Publication date2018
Number of pages1
DOIs
Publication statusPublished - 2018
EventIFAC Conference on Analysis and Design of Hybrid Systems - University of Oxford, Oxford, United Kingdom
Duration: 11 Jul 201813 Jul 2018
http://www.cs.ox.ac.uk/conferences/ADHS18/

Conference

ConferenceIFAC Conference on Analysis and Design of Hybrid Systems
LocationUniversity of Oxford
CountryUnited Kingdom
CityOxford
Period11/07/201813/07/2018
Internet address

Fingerprint

Polynomials
Lyapunov functions
Control systems

Cite this

Hamadneh, T., & Wisniewski, R. (2018). Algorithm for Bernstein Polynomial Control Design. 283. Abstract from IFAC Conference on Analysis and Design of Hybrid Systems, Oxford, United Kingdom. https://doi.org/10.1016/j.ifacol.2018.08.048
Hamadneh, Tareq ; Wisniewski, Rafael. / Algorithm for Bernstein Polynomial Control Design. Abstract from IFAC Conference on Analysis and Design of Hybrid Systems, Oxford, United Kingdom.1 p.
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title = "Algorithm for Bernstein Polynomial Control Design",
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Hamadneh, T & Wisniewski, R 2018, 'Algorithm for Bernstein Polynomial Control Design', Oxford, United Kingdom, 11/07/2018 - 13/07/2018, pp. 283. https://doi.org/10.1016/j.ifacol.2018.08.048

Algorithm for Bernstein Polynomial Control Design. / Hamadneh, Tareq; Wisniewski, Rafael.

2018. 283 Abstract from IFAC Conference on Analysis and Design of Hybrid Systems, Oxford, United Kingdom.

Research output: Contribution to conference without publisher/journalConference abstract for conferenceResearchpeer-review

TY - ABST

T1 - Algorithm for Bernstein Polynomial Control Design

AU - Hamadneh, Tareq

AU - Wisniewski, Rafael

PY - 2018

Y1 - 2018

N2 - This paper considers control synthesis for polynomial control systems. The developed method leans upon Lyapunov stability and Bernstein certificates of positivity. We strive to develop an algorithm that computes a polynomial control and a polynomial Lyaponov function in the simplicial Bernstein form. Subsequently, we reduce the control synthesis problem to a finite number of evaluations of a polynomial within Bernstein coefficient bounds representing controls and Lyapunov functions. As a consequence, the equilibrium is asymptotically stable with this control.

AB - This paper considers control synthesis for polynomial control systems. The developed method leans upon Lyapunov stability and Bernstein certificates of positivity. We strive to develop an algorithm that computes a polynomial control and a polynomial Lyaponov function in the simplicial Bernstein form. Subsequently, we reduce the control synthesis problem to a finite number of evaluations of a polynomial within Bernstein coefficient bounds representing controls and Lyapunov functions. As a consequence, the equilibrium is asymptotically stable with this control.

U2 - 10.1016/j.ifacol.2018.08.048

DO - 10.1016/j.ifacol.2018.08.048

M3 - Conference abstract for conference

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ER -

Hamadneh T, Wisniewski R. Algorithm for Bernstein Polynomial Control Design. 2018. Abstract from IFAC Conference on Analysis and Design of Hybrid Systems, Oxford, United Kingdom. https://doi.org/10.1016/j.ifacol.2018.08.048