Meanings and Applications of Structure in Networks of Dynamic Systems

TL;DR

This chapter explores four different notions of system structure in networks of dynamic systems, focusing on their applications in network reconstruction, vulnerability analysis, and distributed control, primarily within linear time-invariant systems.

Contribution

It clarifies the relationships among various structural concepts and highlights the novel application of the dynamical structure function in control and analysis.

Findings

The dynamical structure function aids in network reconstruction.

It enables vulnerability analysis of networked systems.

It facilitates the synthesis or impossibility proof of structured controllers.

Abstract

This chapter reviews four notions of system structure, three of which are contextual and classic (i.e. the complete computational structure linked to a state space model, the sparsity pattern of a transfer function, and the interconnection of subsystems) and one which is relatively new (i.e. the signal structure of a system's dynamical structure function). Although each of these structural concepts apply to the nonlinear and stochastic setting, this work will focus on linear time invariant systems to distill the key concepts and make their relationships clear. We then discusses three applications of the newest structural form (the signal structure of a system's dynamical structure function): network reconstruction, vulnerability analysis, and a recent result in distributed control that guarantees the synthesis of a stabilizing controller with a specified structure or proves that no such controller exists.