Re-Stabilizing Large-Scale Network Systems Using High-Dimension Low-Sample-Size Data Analysis

Abstract

Dynamical Network Marker (DNM) theory offers an efficient approach to identify warning signals at an early stage for impending critical transitions leading to system deterioration in extensive network systems, utilizing High-Dimension Low-Sample-Size (HDLSS) data. It is crucial to explore strategies for enhancing system stability and preventing critical transitions, a process known as re-stabilization. This paper aims to provide a theoretical basis for re-stabilization using HDLSS data by proposing a computational method to approximate pole placement for re-stabilizing large-scale networks. The proposed method analyzes HDLSS data to extract pertinent information about the network system, which is then used to design feedback gain and input placement for approximate pole placement. The novelty of this method lies in adjusting only the diagonal elements of the system matrix, thus simplifying the re-stabilization process and enhancing its practicality. The method is applicable to systems experiencing either saddle-node bifurcation or Hopf bifurcation. A theoretical analysis was performed to examine the perturbation of the maximum eigenvalues of the system matrix using the proposed approximate pole placement method. We validated the proposed method via simulations based on the Holme-Kim model.