Identification of diffusively coupled linear networks through structured polynomial models
It provides a systematic identification framework for physical dynamic networks with diffusive couplings, which is relevant for control and system identification researchers.
The paper develops a prediction error identification method for diffusively coupled linear networks, represented as undirected graphs, and proposes a multi-step least squares convex optimization algorithm to solve the resulting nonconvex problem, enabling consistent parameter and structure identification.
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.