Design And Application Of Controller For Fuzzy System With Mismatched Membership Function

With the development of modern industry,most practical systems have become from simple,easy-to-describe,computationally inexpensive linear systems to complex,costly nonlinear systems.As a result,the difficult of the nonlinear systems control has been increased,and the existing control methods cannot handle the nonlinear systems effectively.In response to this phenomenon,a large amount of literatures have been published.Abundant control methods,such as fuzzy control,neural network control,sliding mode control,sampling control,adaptive control,etc.,have been proposed.Among these control methods,fuzzy control has played an important role in dealing with the control issues of complex nonlinear systems,and a large amount of literatures about fuzzy control have been published.Takagi-Sugeno(T-S)fuzzy model can be used to deal with nonlinear systems,and it can represent the nonlinear system as a linear combination of a series of local linear subsystems by using the IF-THEN rule,and then,each linear subsystem can be connected according to the membership functions.Therefore,the existing linear system theory can be used to analyze and handle the nonlinear systems.However,the type-1 T-S fuzzy model does not consider that there may be some uncertain factors in the systems,so the membership function of the type-1 T-S fuzzy model is certain and does not have the ability to describe the uncertain factors in the systems.For this reason,the interval type-2(IT2)T-S fuzzy model comes into being.By using the upper and lower bound membership functions and the corresponding weight coefficients of the IT2 T-S fuzzy model,the uncertainties in the systems can be described effectively.However,in the control procedure of the complex nonlinear systems,many factors,such as sensor saturation,data loss,actuator failure,denial-of-service(DoS)attacks,and so on,are inevitably occur in the complex transmission environment such that the control of the systems more difficult.By considering and analyzing the above factors,this paper will focus on the above mentioned factors that can affect the performance and stability of the systems,the details are as follows:Firstly,the development background of T-S fuzzy and some major applications are studied.Then,the stability and performance of the nonlinear systems are analyzed for a class of uncertain nonlinear systems subject to packet loss,sensor saturation,data quantization,and sensor failure.Further,the requirements and significance of the research in this chapter are determined.The techniques and tools to be used in this chapter are also given.Next,the effects of DoS attacks on the networked control systems and partial state unpredictability are mainly considered,and a dynamic output feedback mechanism is constructed to control the networked control systems such that the considered systems are exponentially stable.The uncertainty existing in the networked control systems is effectively described by using the upper and lower membership functions of the IT2 T-S fuzzy model.A class of switching systems are developed in the framework of IT2 T-S fuzzy model for different DoS attacks situations.Based on the average dwell-time method and Lyapunov stability theory,an IT2 fuzzy dynamic output feedback control scheme is proposed so that the considered networked control systems can achieve exponential stability under the conditions of DoS attacks and sensor failures.Finally,the validity of the theoretical results of this chapter is verified by simulation examples.Finally,for a class of quarter vehicle suspension systems,a class of switching control methods are proposed to control the considered suspension systems such that the suspension systems are stable and meet the suspension performance requirements.A T-S fuzzy model is used to describe the considered suspension systems,and a class of mismatched membership functions are used to model the switching controller,which improves the flexibility of the controller design.A new membership functions independent Lyapunov function is used in the stability analysis to judge the stability of the considered suspension systems,thus,the information of the membership function and its derivatives can be utilized to reduce the conservativeness in the systems analysis procedure.In addition,a switching control strategy is proposed in this chapter to ensure the improvement of the vehicle driving comfort and the related suspension performance requirements.Moreover,considering the wear of the actuator and the influence of some external factors,an actuator failure model is introduced in this chapter.Lastly,in the simulation part,simulation example is given to verify the effectiveness and superiority of the proposed approach.