Abstract
This work explores the properties of the edge variant of the graph Laplacian in the context of the edge agreement problem. We show that the edge Laplacian, and its corresponding agreement protocol, provide a useful perspective on the well-known node agreement, or the consensus problem. Specifically, the dynamics induced by the edge Laplacian facilitates a better understanding of the role played by certain subgraphs, e.g., cycles and spanning trees, in the original agreement problem. We also point out a reduced order modeling of the edge agreement as parameterized by the spanning trees of the underlying graph.
| Original language | English |
|---|---|
| Title of host publication | Proceedings of the IEEE Conference on Decision and Control |
| Pages | 2309-2314 |
| Number of pages | 6 |
| DOIs | |
| State | Published - Dec 1 2007 |
| Event | 46th IEEE Conference on Decision and Control 2007, CDC - New Orleans, LA, United States Duration: Dec 12 2007 → Dec 14 2007 |
Other
| Other | 46th IEEE Conference on Decision and Control 2007, CDC |
|---|---|
| Country | United States |
| City | New Orleans, LA |
| Period | 12/12/07 → 12/14/07 |
ASJC Scopus subject areas
- Control and Systems Engineering
- Safety, Risk, Reliability and Quality
- Chemical Health and Safety
Cite this
Agreement via the edge laplacian. / Zelazo, Daniel; Rahmani, Amirreza; Mesbahi, Mehran.
Proceedings of the IEEE Conference on Decision and Control. 2007. p. 2309-2314 4434553.Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - Agreement via the edge laplacian
AU - Zelazo, Daniel
AU - Rahmani, Amirreza
AU - Mesbahi, Mehran
PY - 2007/12/1
Y1 - 2007/12/1
N2 - This work explores the properties of the edge variant of the graph Laplacian in the context of the edge agreement problem. We show that the edge Laplacian, and its corresponding agreement protocol, provide a useful perspective on the well-known node agreement, or the consensus problem. Specifically, the dynamics induced by the edge Laplacian facilitates a better understanding of the role played by certain subgraphs, e.g., cycles and spanning trees, in the original agreement problem. We also point out a reduced order modeling of the edge agreement as parameterized by the spanning trees of the underlying graph.
AB - This work explores the properties of the edge variant of the graph Laplacian in the context of the edge agreement problem. We show that the edge Laplacian, and its corresponding agreement protocol, provide a useful perspective on the well-known node agreement, or the consensus problem. Specifically, the dynamics induced by the edge Laplacian facilitates a better understanding of the role played by certain subgraphs, e.g., cycles and spanning trees, in the original agreement problem. We also point out a reduced order modeling of the edge agreement as parameterized by the spanning trees of the underlying graph.
UR - http://www.scopus.com/inward/record.url?scp=62749188883&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=62749188883&partnerID=8YFLogxK
U2 - 10.1109/CDC.2007.4434553
DO - 10.1109/CDC.2007.4434553
M3 - Conference contribution
AN - SCOPUS:62749188883
SN - 1424414989
SN - 9781424414987
SP - 2309
EP - 2314
BT - Proceedings of the IEEE Conference on Decision and Control
ER -