976 research outputs found
Combinatorial Characterization for Global Identifiability of Separable Networks with Partial Excitation and Measurement
This work focuses on the generic identifiability of dynamical networks with
partial excitation and measurement: a set of nodes are interconnected by
transfer functions according to a known topology, some nodes are excited, some
are measured, and only a part of the transfer functions are known. Our goal is
to determine whether the unknown transfer functions can be generically
recovered based on the input-output data collected from the excited and
measured nodes. We introduce the notion of separable networks, for which global
and so-called local identifiability are equivalent. A novel approach yields a
necessary and sufficient combinatorial characterization for local
identifiability for such graphs, in terms of existence of paths and conditions
on their parity. Furthermore, this yields a necessary condition not only for
separable networks, but for networks of any topology.Comment: 8 pages, 1 figure, article to appear in IEEE Conference on Decision
and Control 202
Tight Bounds for Maximal Identifiability of Failure Nodes in Boolean Network Tomography
We study maximal identifiability, a measure recently introduced in Boolean
Network Tomography to characterize networks' capability to localize failure
nodes in end-to-end path measurements. We prove tight upper and lower bounds on
the maximal identifiability of failure nodes for specific classes of network
topologies, such as trees and -dimensional grids, in both directed and
undirected cases. We prove that directed -dimensional grids with support
have maximal identifiability using monitors; and in the
undirected case we show that monitors suffice to get identifiability of
. We then study identifiability under embeddings: we establish relations
between maximal identifiability, embeddability and graph dimension when network
topologies are model as DAGs. Our results suggest the design of networks over
nodes with maximal identifiability using
monitors and a heuristic to boost maximal identifiability on a given network by
simulating -dimensional grids. We provide positive evidence of this
heuristic through data extracted by exact computation of maximal
identifiability on examples of small real networks
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