A Survey of Resilient Coordination for Cyber-Physical Systems Against Malicious Attacks

TL;DR

This survey analyzes resilient coordination in cyber-physical systems under node-injection attacks, emphasizing MSR-type strategies within a three-layer CPS framework. It develops a taxonomy across physical structure, time-varying network topologies, and communication mechanisms, detailing graph-robustness conditions that guarantee resilient consensus for single- and multi-integrator MASs and leader-follower setups. Applications to resilient containment in multi-robot systems and resilient distributed optimization in smart grids illustrate practical impact, while extensions such as trusted nodes, event/self-triggered, and quantized schemes broaden applicability. The work also discusses limitations of current robustness requirements and proposes future research directions toward nonlinear dynamics, high-dimensional resilience, and formal verification methods.

Abstract

Cyber-physical systems (CPSs) facilitate the integration of physical entities and cyber infrastructures through the utilization of pervasive computational resources and communication units, leading to improved efficiency, automation, and practical viability in both academia and industry. Due to its openness and distributed characteristics, a critical issue prevalent in CPSs is to guarantee resilience in presence of malicious attacks. This paper conducts a comprehensive survey of recent advances on resilient coordination for CPSs. Different from existing survey papers, we focus on the node injection attack and propose a novel taxonomy according to the multi-layered framework of CPS. Furthermore, miscellaneous resilient coordination problems are discussed in this survey. Specifically, some preliminaries and the fundamental problem settings are given at the beginning. Subsequently, based on a multi-layered framework of CPSs, promising results of resilient consensus are classified and reviewed from three perspectives: physical structure, communication mechanism, and network topology. Next, two typical application scenarios, i.e., multi-robot systems and smart grids are exemplified to extend resilient consensus to other coordination tasks. Particularly, we examine resilient containment and resilient distributed optimization problems, both of which demonstrate the applicability of resilient coordination approaches. Finally, potential avenues are highlighted for future research.

Figures (7)

• Figure 1: A multilayered framework for CPSs.
• Figure 2: Main structure of this survey.
• Figure 3: The evolution of malicious attacks injected by a single node.
• Figure 4: Illustrations of different threat models: (a) $1$-total Byzantine model, (b) $1$-local malicious model, and (c) $0.5$-fraction local malicious model.
• Figure 5: Illustrations of different robust network topologies: (a) (2,2)-robust graph, (b) 3-robust graph, and (c) strongly 3-robust graph.

Theorems & Definitions (54)

• Definition 1: Normal agent
• Definition 2: Malicious agent
• Definition 3: Byzantine agent
• Definition 4: $F$-total model
• Definition 5: $F$-local model
• Definition 6: $f$-fraction local model
• Definition 7: Resilient distributed algorithm
• Definition 8: Resilient consensus
• Definition 9: Approximate resilient consensus
• Definition 10: $r$-reachable set