A Systematic Review of Dynamic Localisation of Cyber-Physical Disturbances via Graph Laplacians: Methods, Architectures, and Future Research Directions

Abstract

Cyber-Physical Systems (CPS) are increasingly integral to critical infrastructures such as smart grids, transportation networks, industrial automation, and intelligent communication systems. However, their tightly coupled cyber and physical components expose them to complex disturbances, including faults, anomalies, and cyber-attacks. Efficiently localizing such disturbances in dynamic environments remains a significant research challenge. In recent years, graph-based methods—particularly those leveraging Graph Laplacians—have gained prominence due to their ability to model structural dependencies and dynamic interactions within CPS. This paper presents a systematic review of dynamic localization techniques for cyber-physical disturbances using Graph Laplacian frameworks. The review covers key methodologies, architectural paradigms, and emerging applications from 2018 to 2023. It further categorizes approaches based on spectral graph theory, distributed localization, anomaly detection, and graph learning techniques. A comparative analysis of 30 studies is conducted to evaluate performance, scalability, robustness, and applicability across domains. The paper also highlights existing challenges such as real-time adaptability, data sparsity, and computational complexity. Finally, future research directions are outlined, focusing on integrating Graph Neural Networks (GNNs), hybrid learning models, and explainable AI for enhanced disturbance localization in CPS. This review aims to provide a comprehensive reference for researchers and practitioners working in intelligent security and resilient cyber-physical infrastructures.