Logical Consensus for Distributed and Robust Intrusion Detection

In this paper we introduce a novel consensus mech- anism where agents of a network are able to share logical values, or Booleans, representing their local opinions on e.g. the presence of an intruder or of a fire within an indoor environment. We first formulate the logical consensus problem, and then we review relevant results in the literature on cellular automata and convergence of finite-state iteration maps. Under suitable joint conditions on the visibility of agents and their communication capability, we provide an algorithm for generating a logical linear consensus system that is globally stable. The solution is optimal in terms of the number of messages to be exchanged and the time needed to reach a consensus. Moreover, to cope with possible sensor failure, we propose a second design approach that produces robust logical nonlinear consensus systems tolerating a given maximum number of faults. Finally, we show applicability of the agreement mechanism to a case study consisting of a distributed Intrusion Detection System (IDS).

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