### Jorge Cortés

#### Professor

Network identification with latent nodes via auto-regressive models

E. Nozari, Y. Zhao, J. Cortés

IEEE Transactions on Control of Network Systems 5 (2) (2018), 722-736

### Abstract

We consider linear time-invariant networks with unknown interaction
topology where only a subset of the nodes, termed manifest, can be
directly controlled and observed. The remaining nodes are termed
latent and their number is also unknown. Our goal is to identify the
transfer function of the manifest subnetwork and determine whether
interactions between manifest nodes are direct or mediated by latent
nodes. We show that, if there are no inputs to the latent nodes,
then the manifest transfer function can be approximated arbitrarily
well in the $H_{\infty}$-norm sense by the transfer function of an
auto-regressive model. Motivated by this result, we present a
least-squares estimation method to construct the auto-regressive
model from measured data. We establish that the least-squares
matrix estimate converges in probability to the matrix sequence
defining the desired auto-regressive model as the length of data and
the model order grow. We also show that the least-squares
auto-regressive method guarantees an arbitrarily small
$H_\infty$-norm error in the approximation of the manifest transfer
function, exponentially decaying once the model order exceeds a
certain threshold. Finally, we show that when the latent subnetwork
is acyclic, the proposed method achieves perfect identification of
the manifest transfer function above a specific model order as the
length of the data increases. 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