### Jorge Cortés

#### Professor

Identification of linear networks with latent nodes

Y. Zhao, J. Cortés

Proceedings of the American Control
Conference, Boston, Massachusetts, USA, 2016, pp. 173-178

### Abstract

We study identification of linear networks under the assumption that
only a subset of all the nodes in the network can be observed. The
observable nodes are called manifest nodes and they form the
manifest subnetwork. The unobservable nodes are called latent nodes
and the number of latent nodes is unknown. We explore the
possibility of identifying the transfer function of the manifest
subnetwork and whether an interaction between two manifest nodes is
direct or mediated by latent nodes. In particular, we show that if
the external inputs are injected into a linear network only through
the manifest nodes, then there exists an auto-regressive model whose
transfer function is arbitrarily close to the transfer function of
the manifest subnetwork in the $H_{\infty}$ norm sense. Moreover, we
prove that the least-squares method provides consistent estimate of
the auto-regressive model using the measured states of the observed
nodes. Finally, we show that if the latent subnetwork is acyclic,
then the transfer function of the manifest subnetwork can be
perfectly identified using the least-squares auto-regressive
method. Various examples illustrate our results.

pdf

Mechanical and Aerospace Engineering,
University of California, San Diego

9500 Gilman Dr,
La Jolla, California, 92093-0411

Ph: 1-858-822-7930

Fax: 1-858-822-3107

cortes at ucsd.edu

Skype id:
jorgilliyo