The Stabilization And Synchronization Of Finite-State Fuzzy Cognitive Maps

Fuzzy cognitive maps(FCMs),as the product of the integration of fuzzy logic and neural networks,perform knowledge representation and causal reasoning through fuzzy feedback dynamical systems.In recent years,this intelligent model has been extensively used in many fields such as medical diagnosis,management decision making,and time series prediction.Moreover,with its own multi-input/multi-output graph structure with feedback mechanism,the fuzzy cognitive map has an excellent performance in describing,predicting,and controlling complex nonlinear dynamic systems,and has also become a research hotspot in the control of intelligent bodies such as robots and unmanned aerial vehicles.However,the existing work mainly focuses on the research of control applications based on fuzzy cognitive maps,and there is a lack of relevant theoretical analysis.In order to enrich the theoretical study of fuzzy cognitive map in control field,based on the semi-tensor product(STP)technique of matrix,the algebraic modeling of finite-state fuzzy cognitive map and some control problems such as stabilization and synchronization are discussed in this paper,and the main works are as follows:(1)The global and local stabilization problems under state feedback control of finite-state fuzzy cognitive maps are studied.Firstly,based on the STP matrix technique,the method and process of converting finite-state fuzzy cognitive maps into algebraic form are analyzed;secondly,for the global and local stabilization problems of finite-state fuzzy cognitive maps,the reachable state set of the target state are studies respectively,and an algorithm to calculate the reachable state set based on its related properties and theoretical proofs is proposed;the sufficient conditions for the existence of the state feedback controller are discussed,and the construction algorithm and application method of the corresponding feedback controller are designed.Finally,its feasibility is verified by simulation experiments.(2)The problem of global stabilization under the pinning control of finite-state fuzzy cognitive maps is studied.On the basis of algebraization of the finite-state fuzzy cognitive map,the definition of the reachable state set of the target state is proposed by analyzing its state transfer matrix,and the related properties and theoretical proofs are discussed;based on the above theoretical analysis,the pinning control algorithm based on finite-state fuzzy cognitive map with n concept nodes is designed,and the number and location of controllers is further discussed.Finally,its feasibility is verified by simulation experiments.(3)The problem of complete synchronization of two coupled finite-state fuzzy cognitive maps is studied.The drive-response finite-state fuzzy cognitive maps are represented algebraically using STP,and based on the coupled model,the conditions for the drive-response system to reach complete synchronization are analyzed,then the determination conditions and its sufficiency necessity for model synchronization are discussed,and the construction algorithm for the synchronization of coupled finite-state fuzzy cognitive maps is designed on this basis.Finally,its effectiveness is verified by simulation experiments.