Fuzzy Consensus and Synchronization: Theory and Application to Critical Infrastructure Protection Problems

In this paper the Distributed Consensus and Synchronization problems with fuzzy-valued initial conditions are introduced, in order to obtain a shared estimation of the state of a system based on partial and distributed observations, in the case where such a state is affected by ambiguity and/or vagueness. The Discrete-Time Fuzzy Systems (DFS) are introduced as an extension of scalar fuzzy difference equations and some conditions for their stability and representation are provided. The proposed framework is then applied in the field of Critical Infrastructures; the consensus framework is used to represent a scenario where human operators, each able to observe directly the state of a given infrastructure (or of a given area considering vast and geographically dispersed infrastructures), reach an agreement on the overall situation, whose severity is expressed in a linguistic, fuzzy way; conversely synchronization is used to provide a distributed interdependency estimation system, where an array of interdependency models is synchronized via partial observation.