Algorithm for Bernstein Polynomial Control Design

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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.
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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
DOI
Publication statusPublished - 2018
Publication categoryResearch
Peer-reviewedYes
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
ID: 287874756