Model-Free Dominant Pole Placement for Restabilizing High-Dimensional Network Systems via Small-Sample-Size Data

There is a critical transition before a high-dimensional network system completely deteriorates. The Dynamical Network Marker (DNM) theory has been developed for the early prediction of such critical transitions by only using High-Dimension Small-Sample-Size (HDSSS) data. This article presents a model-free dominant pole placement approach for restabilizing the high-dimensional network systems towards avoidance of critical transitions by early treatment. Instead of traditional model-based pole placement, we present a model-free exact dominant pole placement method with dominant eigenvectors of the system matrix, which can be estimated from HDSSS data of system states. We further introduce two approximations of exact dominant pole placement to reduce the complexity of implementing restabilization. The first one is to approximate the right dominant eigenvector-based pole placement by reducing the number of intervened nodes. The second one is to intervene only in the diagonal part of the system matrix. We conduct theoretical analysis and numerical simulations to investigate the performance of the proposed dominant pole placement method.