Converse Barrier Certificate Theorems

Rafael Wisniewski; Christoffer Sloth

doi:10.1109/TAC.2015.2476155

Converse Barrier Certificate Theorems

Rafael Wisniewski, Christoffer Sloth

Research output: Contribution to journal › Journal article › Research › peer-review

42 Citations (Scopus)

Abstract

This paper shows that a barrier certificate exists for any safe dynamical system. Specifically, we prove converse barrier certificate theorems for a class of structurally stable dynamical systems. Other authors have developed a related result by assuming that the dynamical system has neither singular points nor closed orbits. In this paper, we redefine the standard notion of safety to comply with dynamical systems with multiple singular elements. Hereafter, we prove the converse barrier certificate theorems and highlight the differences between our results and previous work by a number of illustrative examples.

Original language	English
Journal	I E E E Transactions on Automatic Control
Volume	61
Issue number	5
Pages (from-to)	1356-1361
ISSN	0018-9286
DOIs	https://doi.org/10.1109/TAC.2015.2476155
Publication status	Published - May 2016

Access to Document

10.1109/TAC.2015.2476155

AUB Link

Search for the material in Aalborg University Library's search engine

CodeMe: CodeMe - Computer Aided Design Methods for Industrial Automation
Wisniewski, R. & Sloth, C.
01/08/2014 → 31/10/2018
Project: Research

Cite this

@article{62093657303645eba343cf30a95a0289,

title = "Converse Barrier Certificate Theorems",

abstract = "This paper shows that a barrier certificate exists for any safe dynamical system. Specifically, we prove converse barrier certificate theorems for a class of structurally stable dynamical systems. Other authors have developed a related result by assuming that the dynamical system has neither singular points nor closed orbits. In this paper, we redefine the standard notion of safety to comply with dynamical systems with multiple singular elements. Hereafter, we prove the converse barrier certificate theorems and highlight the differences between our results and previous work by a number of illustrative examples.",

author = "Rafael Wisniewski and Christoffer Sloth",

year = "2016",

month = may,

doi = "10.1109/TAC.2015.2476155",

language = "English",

volume = "61",

pages = "1356--1361",

journal = "I E E E Transactions on Automatic Control",

issn = "0018-9286",

publisher = "IEEE",

number = "5",

}

TY - JOUR

T1 - Converse Barrier Certificate Theorems

AU - Wisniewski, Rafael

AU - Sloth, Christoffer

PY - 2016/5

Y1 - 2016/5

N2 - This paper shows that a barrier certificate exists for any safe dynamical system. Specifically, we prove converse barrier certificate theorems for a class of structurally stable dynamical systems. Other authors have developed a related result by assuming that the dynamical system has neither singular points nor closed orbits. In this paper, we redefine the standard notion of safety to comply with dynamical systems with multiple singular elements. Hereafter, we prove the converse barrier certificate theorems and highlight the differences between our results and previous work by a number of illustrative examples.

AB - This paper shows that a barrier certificate exists for any safe dynamical system. Specifically, we prove converse barrier certificate theorems for a class of structurally stable dynamical systems. Other authors have developed a related result by assuming that the dynamical system has neither singular points nor closed orbits. In this paper, we redefine the standard notion of safety to comply with dynamical systems with multiple singular elements. Hereafter, we prove the converse barrier certificate theorems and highlight the differences between our results and previous work by a number of illustrative examples.

U2 - 10.1109/TAC.2015.2476155

DO - 10.1109/TAC.2015.2476155

M3 - Journal article

SN - 0018-9286

VL - 61

SP - 1356

EP - 1361

JO - I E E E Transactions on Automatic Control

JF - I E E E Transactions on Automatic Control

IS - 5

ER -

Converse Barrier Certificate Theorems

Abstract

Access to Document

AUB Link

Fingerprint

Projects

CodeMe: CodeMe - Computer Aided Design Methods for Industrial Automation

Cite this