Logical consensus for distributed network agreement

In this paper we introduce a novel consensus mechanism 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. Under suitable joint conditions on agents¿ visibility and communication capability, we provide an algorithm 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 maximum number of faults. Finally, we show applicability of the agreement mechanism to a distributed intrusion detection system (IDS).