Identification of diffusively coupled linear networks through structured polynomial models

TL;DR

This paper presents a method to identify the structure and parameters of diffusively coupled linear networks using polynomial models and a novel convex optimization algorithm.

Contribution

It adapts prediction error identification for symmetric diffusive networks and introduces a multi-step least squares algorithm for parameter estimation.

Findings

Successfully identifies network structure and parameters.

Provides a convex optimization approach for the nonconvex problem.

Applicable to physical dynamic networks with diffusive couplings.

Abstract

Physical dynamic networks most commonly consist of interconnections of physical components that can be described by diffusive couplings. These diffusive couplings imply that the cause-effect relationships in the interconnections are symmetric and therefore physical dynamic networks can be represented by undirected graphs. This paper shows how prediction error identification methods developed for linear time-invariant systems in polynomial form can be configured to consistently identify the parameters and the interconnection structure of diffusively coupled networks. Further, a multi-step least squares convex optimization algorithm is developed to solve the nonconvex optimization problem that results from the identification method.