Herdable Systems over Signed, Directed Graphs

Sebastian F. Ruf, Magnus Egerstedt, Jeff S. Shamma

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This paper considers the notion of herdability, a set-based reachability condition, which asks whether the state of a system can be controlled to be element-wise larger than a non-negative threshold. The basic theory of herdable systems is presented, including a necessary and sufficient condition for herdability. This paper then considers the impact of the underlying graph structure of a linear system on the herdability of the system, for the case where the graph is represented as signed and directed. By classifying nodes based on the length and sign of walks from an input, we find a class of completely herdable systems as well as provide a complete characterization of nodes that can be herded in systems with an underlying graph that is a directed out-branching rooted at a single input.

Original languageEnglish (US)
Title of host publication2018 Annual American Control Conference, ACC 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1807-1812
Number of pages6
ISBN (Print)9781538654286
DOIs
StatePublished - Aug 9 2018
Externally publishedYes
Event2018 Annual American Control Conference, ACC 2018 - Milwauke, United States
Duration: Jun 27 2018Jun 29 2018

Publication series

NameProceedings of the American Control Conference
Volume2018-June
ISSN (Print)0743-1619

Other

Other2018 Annual American Control Conference, ACC 2018
CountryUnited States
CityMilwauke
Period6/27/186/29/18

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

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