Paper Info
Title
Dynamic Coverage Verification in Mobile Sensor Networks Via Switched Higher Order Laplacians
Abstract
In this paper, we study the problem of verifying dynamic coverage in mobile sensor networks using certain switched linear systems. These switched systems describe the flow of discrete differential forms on time-evolving simplicial complexes. The simplicial complexes model the connectivity of agents in the network, and the homology groups of the simplicial complexes provides information about the coverage properties of the network. Our main result states that the asymptotic stability the switched linear system implies that every point of the domain covered by the mobile sensor nodes is visited infinitely often, hence verifying dynamic coverage. The enabling mathematical technique for this result is the theory of higher order Laplacian operators, which is a generalization of the graph Laplacian used in spectral graph theory and continuous-time consensus problems.
Year
Venue
Keywords
2007
Robotics: Science and Systems
i. i ntroduction and motivation,graph laplacian,spectral graph theory,higher order,simplicial complex,asymptotic stability,consensus problem,differential forms
Field
DocType
Citations 
Singular homology,Spectral graph theory,Linear system,Computer science,Differential form,Exponential stability,Operator (computer programming),Artificial intelligence,Discrete mathematics,Computer vision,Topology,Laplacian matrix,Laplace operator
Conference
9
PageRank 
References 
Authors
0.75
15
2
Name
Order
Citations
PageRank
Abubakr Muhammad130830.59
Ali Jadbabaie24806581.69