Modeling And Application Of Fuzzy Control System Based-on Boolean Network

Most of the real systems existing in the objective world are nonlinear systems,so that the control theory of nonlinear system and its applied research are always the hot topics of scholars in the field of control.Because of the complexity,multivariable,coupling and other factors of nonlinear systems,it is difficult to set up accurate mathematical models and analyze dynamic performance of nonlinear systems.On the other hand,as an essential model of the biological system,the nonlinear Boolean network system has become a hot topic in the crossed academics between biology and control systems.In this thesis,the mathematical modeling and performance analysis algorithms of nonlinear Boolean network systems are studied.The main contents are organized as follows.(1)Firstly,the research background and significance are described about modeling and analysis of the fuzzy control systems,based on the nonlinear Boolean network.This chapter introduces the existing methods of nonlinear system modeling and the research status of the Boolean network and fuzzy control and also analyzes the reasons why fuzzy dynamic models are used for the modeling of nonlinear Boolean networks.Finally,the main idea of this thesis and contents of each chapter are given.(2)In order to establish the fuzzy dynamic Boolean network control system models,the matrix Semi-Tensor Product theories is first introduced.On the base of the matrix SemiTensor Product theories,the logic operations of the Boolean Control Network are transformed into the algebraic operations.Accordingly,using the fuzzy dynamic model,nonlinear fuzzy modeling of the Boolean network is designed.In each rule of the dynamic fuzzy inference processes,the Boolean network control system is locally linear.And then the local model and global model of the system are established respectively.From the local and global meanings of the system,the basis of dynamic properties are analyzed,such as controllability,observability and stability etc.(3)The dynamic characteristics of nonlinear systems include controllability,observability and stability,etc.Based on the fuzzy dynamic Boolean network model,theprimary dynamic performances,including controllability,observability and stability etc.are analyzed separately for the local model and the global model.Finally,a numerical example is presented about a multiple-input multiple-output nonlinear Boolean network system.As a result,the validity of the method is verified.(4)State feedback can adequately reflect the internal characteristics of the system.The state feedback control design of the fuzzy dynamic Boolean network control system is studied.And using the fuzzy Lyapunov function,the pole of the fuzzy dynamic Boolean network control system is configured.A simulation example is given to verify the feasibility of designing the state feedback to improve the systemic performance.(5)In order to further verify the effectiveness of performance analysis and design of fuzzy dynamic Boolean network model,we try to apply this novel model into a simple lighting system.Firstly,the fuzzy dynamic Boolean network model of the system is built,and then it is analyzed and designed to make the system meet the different requirements of the lighting system.(6)Finally,the achieved research results in this thesis are summarized.Because of the research in this content,several directions for the further study of fuzzy dynamic Boolean network models in the future are proposed.