Graph-theoretic approaches for analyzing the resilience of distributed control systems: A tutorial and survey

As the scale of distributed control systems over networks increases and interactions between different subsystems become more sophisticated, questions of the resilience of such networks to attacks and faults increase in importance. The need to adapt (and redefine) classical system and control-theoretic notions to answer such questions using the language of graphs has recently started to gain attention as a fertile and important area of research. This paper presents an overview of graph-theoretic methods for analyzing the resilience of distributed control systems. We survey distributed algorithms that have been proposed to solve a variety of problems in networked systems, and summarize their resilience against adversarial actions in the context of the structure of the underlying networks. We also discuss graph-theoretic methods to quantify the attack impact, and reinterpret some system-theoretic notions of robustness from a graph-theoretic standpoint to mitigate the impact of the attacks. We conclude by introducing some avenues for further research in this field.& COPY; 2023 Elsevier Ltd. All rights reserved.