Herdable Systems Over Signed, Directed Graphs

Handle URI:
http://hdl.handle.net/10754/627562
Title:
Herdable Systems Over Signed, Directed Graphs
Authors:
Ruf, Sebastian F.; Egerstedt, Magnus; Shamma, Jeff S. ( 0000-0001-5638-9551 )
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.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Electrical Engineering Program
Publisher:
arXiv
Issue Date:
11-Apr-2018
ARXIV:
arXiv:1804.04230
Type:
Preprint
Additional Links:
http://arxiv.org/abs/1804.04230v1; http://arxiv.org/pdf/1804.04230v1
Appears in Collections:
Other/General Submission; Electrical Engineering Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorRuf, Sebastian F.en
dc.contributor.authorEgerstedt, Magnusen
dc.contributor.authorShamma, Jeff S.en
dc.date.accessioned2018-04-19T10:45:31Z-
dc.date.available2018-04-19T10:45:31Z-
dc.date.issued2018-04-11en
dc.identifier.urihttp://hdl.handle.net/10754/627562-
dc.description.abstractThis 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.en
dc.publisherarXiven
dc.relation.urlhttp://arxiv.org/abs/1804.04230v1en
dc.relation.urlhttp://arxiv.org/pdf/1804.04230v1en
dc.rightsArchived with thanks to arXiven
dc.titleHerdable Systems Over Signed, Directed Graphsen
dc.typePreprinten
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentElectrical Engineering Programen
dc.eprint.versionPre-printen
dc.contributor.institutionSchool of Electrical and Computer Engineering, Georgia Institute of Technologyen
dc.identifier.arxividarXiv:1804.04230en
kaust.authorShamma, Jeff S.en
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