Resilience against misbehaving nodes in asynchronous networks

Abstract

Network systems are one of the most active research areas in the engineering community as they feature a paradigm shift from centralized to distributed control and computation. When dealing with network systems, a fundamental challenge is to ensure their functioning even when some of the network nodes do not operate as intended due to faults or attacks. The objective of this paper is to address the problem of resilient consensus in a context where the nodes have their own clocks, possibly operating in an asynchronous way, and can make updates at arbitrary time instants. The results represent a first step towards the development of resilient event-triggered and self-triggered coordination protocols. IntroductionNetwork systems are one of the most active research areas in the engineering community as they feature a paradigm shift from centralized to distributed control and computation. When dealing with network systems, a fundamental challenge is to ensure their functioning even when some of the network units (nodes) do not operate as intended due to faults or attacks. The main difficulty originates from the fact that normal (non-misbehaving) nodes can receive, process, and spread erroneous data coming from misbehaving nodes with the consequence that a failure in one point of the network can compromise the whole network functioning.The prototypical problem to study resilience in the presence of misbehaving nodes is the so-called consensus problem [1], which forms the foundation for distributed computing. In resilient consensus, each node is assumed to be aware of only local information available from its neighbors and the goal is to make sure that normal nodes eventually reach a common value despite the presence of misbehaving nodes. The resilient consensus problem has a long history, and it has been investigated first by computer scientists [2,3], usually under the hypothesis that the network graph is complete, that is assuming an allto-all communication structure. More recently, thanks to the widespread of consensus-based applications, this problem has attracted a lot of interest also within the engineering community, mostly in connection with the goal of delineating the minimal connectivity hypotheses that are needed to secure consensus.In [4], the authors consider mean subsequence reduced (MSR) algorithms and define a graph-theoretic property, referred to as network robustness, which charactherizes necessary and sufficient connectivity hypotheses under which normal nodes can reach consensus using only local information available from their neighbors. The results indicate that, while the communication graph should possess a certain degree of redundancy, completeness of the communication graph is not necessary even for very general types of misbehavior. The results of [4] have been extended in many venues. Examples include methods for handling time-varying networks [5], double-integrator systems [6], sparse communication graphs [7] as well as methods for identifying the robustness of specific classes of networks ...

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“…To reduce the communication burden, E‐MSR algorithm, which introduced event‐based update rule to MSR‐type algorithms, was proposed in Reference 11 for first‐order multiagent systems to reach resilient consensus. In References 12‐16, resilient consensus results were given in continuous‐time setting. In Reference 12, ARC‐P algorithm, which is a continuous‐time variation of the MSR, was proposed to solve asymptotic consensus under totally bounded malicious model.…”