DocumentCode :
592353
Title :
Cycles and sparse design of consensus networks
Author :
Zelazo, D. ; Schuler, Steffen ; Allgower, F.
Author_Institution :
Inst. for Syst. Theor. & Autom. Control, Univ. of Stuttgart, Stuttgart, Germany
fYear :
2012
fDate :
10-13 Dec. 2012
Firstpage :
3808
Lastpage :
3813
Abstract :
This work considers the role that cycles play in consensus networks. We show how the presence of cycles improve the H2 performance of the consensus network. In particular, we provide an explicit combinatorial characterization relating the length of cycles to the improvement in the performance of the network. This analysis points to a general trade-off between the length of the cycle and how many edges the cycle shares with other cycles. These analytic results are then used to motivate a design procedure for consensus networks based on an ℓ1 relaxation. This relaxation method leads to sparse and {0, 1}-solutions for the design of consensus graphs. A feature of the ℓ1 relaxation is the ability to include weighting terms in the objective. The choice of weighting functions are related to the combinatorial properties of the graph. The applicability of this scheme is then shown via a set of numerical examples.
Keywords :
graph theory; network theory (graphs); relaxation theory; combinatorial characterization; combinatorial property; consensus graphs; consensus networks; design procedure; network performance; relaxation method; sparse design; weighting functions; weighting terms; Correlation; Eigenvalues and eigenfunctions; Laplace equations; Noise; Optimization; Protocols; Vectors;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Decision and Control (CDC), 2012 IEEE 51st Annual Conference on
Conference_Location :
Maui, HI
ISSN :
0743-1546
Print_ISBN :
978-1-4673-2065-8
Electronic_ISBN :
0743-1546
Type :
conf
DOI :
10.1109/CDC.2012.6426450
Filename :
6426450
Link To Document :
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