TY - GEN
T1 - Herdable Systems over Signed, Directed Graphs
AU - Ruf, Sebastian F.
AU - Egerstedt, Magnus
AU - Shamma, Jeff S.
N1 - Publisher Copyright:
© 2018 AACC.
PY - 2018/8/9
Y1 - 2018/8/9
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85052596811&partnerID=8YFLogxK
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U2 - 10.23919/ACC.2018.8431101
DO - 10.23919/ACC.2018.8431101
M3 - Conference contribution
AN - SCOPUS:85052596811
SN - 9781538654286
T3 - Proceedings of the American Control Conference
SP - 1807
EP - 1812
BT - 2018 Annual American Control Conference, ACC 2018
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2018 Annual American Control Conference, ACC 2018
Y2 - 27 June 2018 through 29 June 2018
ER -