| A complex network is a large-scale network with a complex topological structure and dynamic behaviors.Many physical and chemical reactions can produce reaction-diffusion phenomenon.it is necessary to study the reaction-diffusion equation.In recent years,the topological structure and dynamic behavior of complex networks with reaction-diffusion terms have attracted wide attention of scholars,especially the synchronization problem.In this paper,T-S fuzzy model is used for fuzzy modeling of complex networks with reaction-diffusion terms.The synchronization of fuzzy complex networks with constant coefficients or variable coefficients is studied by using fuzzy control and non-matching premise membership functions.The T-S fuzzy model and the fuzzy state-feedback controller of the system do not have the same membership functions and/or the same number of fuzzy rules,and a synchronization method based on the membership functions is presented.The main contents of the thesis are as followsIn Chapter 1,the background and research status of complex networks and T-S fuzzy systems with reaction-diffusion terms are summarizedIn the second chapter,a state-feedback controller is designed for constant-coefficient fuzzy complex networks with the reaction-diffusion term to synchronize the closed-loop networks.With the support of Green's formula,Lyapunov stability theory and some matrix inequality techniques,the sufficient conditions for synchronization are obtained,and the synchronization conditions are presented in the form of linear matrix inequalities(LMIs).In addition,this chapter approximates the membership function of the fuzzy model and the fuzzy controller by using piecewise linear membership functions,whose membership degrees are controlled by a finite number of sample points,so that the synchronization of the network can be determined by checking the properties of the network at the sample points only.When the characteristics of membership functions are introduced into synchronization analysis,the sufficient condition is less conservative in some cases.Finally,the LMI toolbox of MATLAB is used to simulate the results and verify the correctness of the theoretical analysisIn the third chapter,T-S fuzzy model is used for fuzzy modeling of complex networks with variable coefficients with reaction-diffusion terms,and a fuzzy state-feedback controller is designed.By using inequality technology,Lyapunov stability theory and appropriate hypothesis,the synchronization criteria of the membership-function-independent case and the membership-function-dependent case are both given.In the analysis of the synchronization of the membership function,the global boundary information of the membership function is brought into the analysis of the synchronization by relaxation matrix,and the property of the upper and lower bound of the product term of membership function is used to relax the result of the analysis of the synchronization.Finally,the LMI toolbox of MATLAB is used to verify the feasibility of the synchronization strategy proposed in this paper.The fourth chapter summarizes the thesis and looks forward to the future research work. |
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