Graph-theoretic analysis and synthesis of relative sensing networks

Daniel Zelazo; Mehran Mesbahi

doi:https://doi.org/10.1109/TAC.2010.2085312

Graph-theoretic analysis and synthesis of relative sensing networks

Research output: Contribution to journal › Article › peer-review

Abstract

This work provides a general framework for the analysis and synthesis of a class of relative sensing networks (RSNs) in the context of its H₂ and H_∞ performance. We consider RSNs with homogeneous and heterogeneous agent dynamics. In both cases, explicit graph theoretic expressions and bounds for the H₂ and H_∞ performance are derived. The H₂ performance turns out to be a function of the number of edges in the graph, whereas the H_∞ performance is structure dependent and related to the spectral radius of the graph Laplacian. The analysis results are then used to develop synthesis methods for RSNs. An optimal topology is designed using the Kruskal's Algorithm for H₂ performance, and a semi-definite program for the H_∞ performance of uncertain RSNs.

Original language	English
Article number	5598522
Pages (from-to)	971-982
Number of pages	12
Journal	IEEE Transactions on Automatic Control
Volume	56
Issue number	5
DOIs	https://doi.org/10.1109/TAC.2010.2085312
State	Published - May 2011
Externally published	Yes

Keywords

Combinatorial optimization
H and H performance
graph theory
relative sensing networks
semi-definite programming

All Science Journal Classification (ASJC) codes

Control and Systems Engineering
Computer Science Applications
Electrical and Electronic Engineering

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https://doi.org/10.1109/TAC.2010.2085312

Cite this

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title = "Graph-theoretic analysis and synthesis of relative sensing networks",

abstract = "This work provides a general framework for the analysis and synthesis of a class of relative sensing networks (RSNs) in the context of its H2 and H∞ performance. We consider RSNs with homogeneous and heterogeneous agent dynamics. In both cases, explicit graph theoretic expressions and bounds for the H2 and H∞ performance are derived. The H2 performance turns out to be a function of the number of edges in the graph, whereas the H∞ performance is structure dependent and related to the spectral radius of the graph Laplacian. The analysis results are then used to develop synthesis methods for RSNs. An optimal topology is designed using the Kruskal's Algorithm for H2 performance, and a semi-definite program for the H∞ performance of uncertain RSNs.",

keywords = "Combinatorial optimization, H and H performance, graph theory, relative sensing networks, semi-definite programming",

author = "Daniel Zelazo and Mehran Mesbahi",

note = "Funding Information: Manuscript received August 12, 2009; revised April 29, 2010 and September 09, 2010; accepted September 09, 2010. Date of publication October 11, 2010; date of current version May 11, 2011. This work was supported in part by the NSF under Grant ECS-0501606. Recommended by Associate Editor M. Pran-dini.",

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doi = "https://doi.org/10.1109/TAC.2010.2085312",

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AU - Mesbahi, Mehran

N1 - Funding Information: Manuscript received August 12, 2009; revised April 29, 2010 and September 09, 2010; accepted September 09, 2010. Date of publication October 11, 2010; date of current version May 11, 2011. This work was supported in part by the NSF under Grant ECS-0501606. Recommended by Associate Editor M. Pran-dini.

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N2 - This work provides a general framework for the analysis and synthesis of a class of relative sensing networks (RSNs) in the context of its H2 and H∞ performance. We consider RSNs with homogeneous and heterogeneous agent dynamics. In both cases, explicit graph theoretic expressions and bounds for the H2 and H∞ performance are derived. The H2 performance turns out to be a function of the number of edges in the graph, whereas the H∞ performance is structure dependent and related to the spectral radius of the graph Laplacian. The analysis results are then used to develop synthesis methods for RSNs. An optimal topology is designed using the Kruskal's Algorithm for H2 performance, and a semi-definite program for the H∞ performance of uncertain RSNs.

AB - This work provides a general framework for the analysis and synthesis of a class of relative sensing networks (RSNs) in the context of its H2 and H∞ performance. We consider RSNs with homogeneous and heterogeneous agent dynamics. In both cases, explicit graph theoretic expressions and bounds for the H2 and H∞ performance are derived. The H2 performance turns out to be a function of the number of edges in the graph, whereas the H∞ performance is structure dependent and related to the spectral radius of the graph Laplacian. The analysis results are then used to develop synthesis methods for RSNs. An optimal topology is designed using the Kruskal's Algorithm for H2 performance, and a semi-definite program for the H∞ performance of uncertain RSNs.

KW - Combinatorial optimization

KW - H and H performance

KW - graph theory

KW - relative sensing networks

KW - semi-definite programming

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DO - https://doi.org/10.1109/TAC.2010.2085312

M3 - مقالة

SN - 0018-9286

VL - 56

SP - 971

EP - 982

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

IS - 5

M1 - 5598522

ER -

Graph-theoretic analysis and synthesis of relative sensing networks

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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