In this paper the synchronization of a network of identical systems with fuzzy initial conditions is introduced, as a convenient framework to obtain a shared estimation of the state of the system based on partial and distributed observations, in the case where such a state is affected by ambiguity and/or vagueness. After discussing the synchronization of crisp systems, providing a criteria to find the information sharing law that lets the network converge to a shared trajectory, Discrete-Time Fuzzy Systems (DFS) are introduced as an extension of scalar fuzzy difference equations. Besides providing a stability condition for a general DFS, in the linear case it is proven that, under a non-negativity assumption for the coefficients of the system, the fuzzyfication of the initial conditions does not compromise the stability of the crisp system. A framework for the synchronization of arrays of linear DFS is then introduced, proving that the crisp synchronization is a particular case of the proposed approach. Finally, a case study in the field of Critical Infrastructure Protection is provided

Distributed synchronization under uncertainty: a Fuzzy Approach

Oliva G;Setola R
2012-01-01

Abstract

In this paper the synchronization of a network of identical systems with fuzzy initial conditions is introduced, as a convenient framework to obtain a shared estimation of the state of the system based on partial and distributed observations, in the case where such a state is affected by ambiguity and/or vagueness. After discussing the synchronization of crisp systems, providing a criteria to find the information sharing law that lets the network converge to a shared trajectory, Discrete-Time Fuzzy Systems (DFS) are introduced as an extension of scalar fuzzy difference equations. Besides providing a stability condition for a general DFS, in the linear case it is proven that, under a non-negativity assumption for the coefficients of the system, the fuzzyfication of the initial conditions does not compromise the stability of the crisp system. A framework for the synchronization of arrays of linear DFS is then introduced, proving that the crisp synchronization is a particular case of the proposed approach. Finally, a case study in the field of Critical Infrastructure Protection is provided
Critical infrastructures; Fuzzy systems; Synchronization
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12610/6086
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