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— We introduce the concept of matrix-valued effective resistance for undirected matrix-weighted graphs. Effective resistances are defined to be the square blocks that appear in the diagonal of the inverse of the matrix-weighted Dirichlet graph Laplacian matrix. However, they can also be obtained from a " generalized " electrical network that is constructed(More)
SUMMARY We study the stability and robustness of a large platoon of vehicles, where each vehicle is modeled as a double integrator, for two decentralized control architectures: predecessor-following and symmetric bidirectional. In the predecessor-following architecture, the control action on each agent only depends on the information from its immediate(More)
We consider the problem of estimating vector-valued variables from noisy "relative" measurements. The measurement model can be expressed in terms of a graph, whose nodes correspond to the variables being estimated and the edges to noisy measurements of the difference between the two variables. We take the value of one particular variable as a reference and(More)
We consider the problem of estimating vector-valued variables from noisy " relative " measurements. The measurement model can be expressed in terms of a graph, whose nodes correspond to the variables being estimated and the edges to noisy measurements of the difference between the two variables. This type of measurement model appears in several sensor(More)
Loss of connectivity in deployed wireless sensor networks can be quite disastrous for the network. A "cut" (which separates the network into two or more components incapable of communicating with each other) is usually hard to detect. An algorithm which enables each node in the network to detect whether a cut has occurred anywhere in the network is(More)
Sensor networks are collections of interconnected nodes equipped with sensing and computing capability that are deployed in a geographic area to perform some form of monitoring tasks. Networks consisting of a large collection of such nodes are currently under development or envisioned for the near future [1, 2]. Usually a node can communicate with only a(More)
We study the stability margin of a vehicular formation with distributed control, in which the control at each vehicle only depends on the information from its neighbors in an information graph. We consider a D-dimensional lattice as information graph, of which the 1-D platoon is a special case. The stability margin is measured by the real part of the least(More)