The synchronization of K-valued Fuzzy cognitive maps

Fuzzy cognitive maps (FCMs) with the abilities of knowledge representation and causal reasoning have been widely applied in the control-related fields of multi-agent systems (MAS), such as the mobile robots and unmanned aerial vehicles (UAVs). From the perspective of system applications, the cooperative control of group behaviors is a meaningful topic in this community, where the synchronization of agents is one of fundamental issues. However, how to achieve the synchronization of FCM-based control mechanism is still an open problem. In this article, two finite state fuzzy cognitive map systems with unidirectional coupling in the drive-response configuration are introduced. By utilizing matrix semi-tensor product (STP), the coupling dynamical systems are transformed into algebraic forms, based on which the necessary and sufficient conditions for complete synchronization are presented. The corresponding theoretical proofs are given and quantitative analysis are implemented. Finally, several experiments are given to prove the effectiveness of the proposed methods.