Controllable Subspaces in Structured Networks of Hierarchical Directed Acyclic Graphs: Controllability of Individual Nodes

TL;DR

This paper introduces the Fixed Strongly Structurally Controllable Subspace (FSSCS) concept to characterize controllable subspaces in hierarchical directed acyclic graphs, advancing understanding of node controllability robustness.

Contribution

It defines FSSC nodes based on FSSCS and provides a method to determine the SSCS dimension in hierarchical DAGs, improving controllability analysis.

Findings

Identifies necessary and sufficient conditions for FSSC nodes.

Provides a method to compute SSCS dimension in hierarchical DAGs.

Enhances understanding of controllability robustness in structured networks.

Abstract

Within the context of structured networks, this paper introduces the concept of the Fixed Strongly Structurally Controllable Subspace (FSSCS), enabling a comprehensive characterization of controllable subspaces. From a graph-theoretical viewpoint, the paper defines Fixed Strongly Structurally Controllable (FSSC) nodes based on the FSSCS concept and establishes the necessary and sufficient conditions for their identification. This paper proposes a method for determining the exact dimension of the Strongly Structurally Controllable Subspace (SSCS) in hierarchical directed acyclic graphs, employing a blend of graph-theoretical approaches and controllability matrix analyses. This approach not only facilitates the identification of FSSC nodes but also enhances our understanding of the robustness of node controllability against variations in network parameters within structured networks, marking a significant advancement in the field of strong structural controllability of individual nodes.