A graph-theoretic approach to the reach control problem

Melkior Ornik; Mireille E. Broucke

doi:10.1109/CDC.2017.8264392

A graph-theoretic approach to the reach control problem

Melkior Ornik, Mireille E. Broucke

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

Abstract

This paper establishes new necessary and sufficient conditions for the solvability of the Reach Control Problem (RCP). The RCP seeks to drive the trajectories of a control system defined on a simplex to leave this simplex through a predetermined facet. This paper takes a novel approach to the RCP, transforming it into a problem in positive system theory. Using the notions of Z-matrices and graph theory, this results in a number of new necessary and sufficient conditions for the solvability of the RCP. In parallel, we also examine open-loop equilibria in the RCP, and provide a number of necessary and sufficient conditions for their existence.

Original language	English (US)
Title of host publication	2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	4952-4957
Number of pages	6
ISBN (Electronic)	9781509028733
DOIs	https://doi.org/10.1109/CDC.2017.8264392
State	Published - Jun 28 2017
Externally published	Yes
Event	56th IEEE Annual Conference on Decision and Control, CDC 2017 - Melbourne, Australia Duration: Dec 12 2017 → Dec 15 2017

Publication series

Name	2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
Volume	2018-January

Other

Other	56th IEEE Annual Conference on Decision and Control, CDC 2017
Country/Territory	Australia
City	Melbourne
Period	12/12/17 → 12/15/17

ASJC Scopus subject areas

Decision Sciences (miscellaneous)
Industrial and Manufacturing Engineering
Control and Optimization

Online availability

10.1109/CDC.2017.8264392

Library availability

Discover UIUC Full Text

Cite this

A graph-theoretic approach to the reach control problem. / Ornik, Melkior; Broucke, Mireille E.
2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017. Institute of Electrical and Electronics Engineers Inc., 2017. p. 4952-4957 (2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017; Vol. 2018-January).

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

Ornik, M & Broucke, ME 2017, A graph-theoretic approach to the reach control problem. in 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017. 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017, vol. 2018-January, Institute of Electrical and Electronics Engineers Inc., pp. 4952-4957, 56th IEEE Annual Conference on Decision and Control, CDC 2017, Melbourne, Australia, 12/12/17. https://doi.org/10.1109/CDC.2017.8264392

@inproceedings{90345b331d374dfea72e6675bcff6f14,

title = "A graph-theoretic approach to the reach control problem",

abstract = "This paper establishes new necessary and sufficient conditions for the solvability of the Reach Control Problem (RCP). The RCP seeks to drive the trajectories of a control system defined on a simplex to leave this simplex through a predetermined facet. This paper takes a novel approach to the RCP, transforming it into a problem in positive system theory. Using the notions of Z-matrices and graph theory, this results in a number of new necessary and sufficient conditions for the solvability of the RCP. In parallel, we also examine open-loop equilibria in the RCP, and provide a number of necessary and sufficient conditions for their existence.",

author = "Melkior Ornik and Broucke, {Mireille E.}",

note = "Publisher Copyright: {\textcopyright} 2017 IEEE.; 56th IEEE Annual Conference on Decision and Control, CDC 2017 ; Conference date: 12-12-2017 Through 15-12-2017",

year = "2017",

month = jun,

day = "28",

doi = "10.1109/CDC.2017.8264392",

language = "English (US)",

series = "2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "4952--4957",

booktitle = "2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017",

address = "United States",

}

TY - GEN

T1 - A graph-theoretic approach to the reach control problem

AU - Ornik, Melkior

AU - Broucke, Mireille E.

PY - 2017/6/28

Y1 - 2017/6/28

N2 - This paper establishes new necessary and sufficient conditions for the solvability of the Reach Control Problem (RCP). The RCP seeks to drive the trajectories of a control system defined on a simplex to leave this simplex through a predetermined facet. This paper takes a novel approach to the RCP, transforming it into a problem in positive system theory. Using the notions of Z-matrices and graph theory, this results in a number of new necessary and sufficient conditions for the solvability of the RCP. In parallel, we also examine open-loop equilibria in the RCP, and provide a number of necessary and sufficient conditions for their existence.

AB - This paper establishes new necessary and sufficient conditions for the solvability of the Reach Control Problem (RCP). The RCP seeks to drive the trajectories of a control system defined on a simplex to leave this simplex through a predetermined facet. This paper takes a novel approach to the RCP, transforming it into a problem in positive system theory. Using the notions of Z-matrices and graph theory, this results in a number of new necessary and sufficient conditions for the solvability of the RCP. In parallel, we also examine open-loop equilibria in the RCP, and provide a number of necessary and sufficient conditions for their existence.

UR - http://www.scopus.com/inward/record.url?scp=85046115641&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85046115641&partnerID=8YFLogxK

U2 - 10.1109/CDC.2017.8264392

DO - 10.1109/CDC.2017.8264392

M3 - Conference contribution

AN - SCOPUS:85046115641

T3 - 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017

SP - 4952

EP - 4957

BT - 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 56th IEEE Annual Conference on Decision and Control, CDC 2017

Y2 - 12 December 2017 through 15 December 2017

ER -

A graph-theoretic approach to the reach control problem

Abstract

Publication series

Other

ASJC Scopus subject areas

Online availability

Library availability

Related links

Fingerprint

Cite this