Research On Local Stabilization And Fault Diagnosis For T-S Fuzzy Systems

Nonlinearities widely exist in control systems,such as,power electronic systems,aerospace systems,chemical process systems,and so on.This increases the difficulties of analysis and synthesis for systems.For dealing with the nonlinear problem,Takagi and Sugeno proposed Takagi-Sugeno(T-S)fuzzy model in 1985.T-S fuzzy systems have a good ability to approximate the nonlinear functions,meanwhile,under the framework of T-S fuzzy systems,many excellent results related to the linear systems could be used for dealing with the problem of nonlinear systems.During the past decades,T-S fuzzy systems have received considerable attentions and many valuable results have been reported.However,in this research field,there are still some problems,which have not been solved yet.For example,in the conventional methods,it is often assumed that the system states can be restricted in a compact set.And then based on the assumption,the problems for T-S fuzzy systems are studied.However,in practice,the assumption is hard to be satisfied.Due to the existence of the factors,such as disturbances or uncertainties,the system states may exceed the specified region such that T-S fuzzy model is not able to represent the nonlinear systems effectively.Therefore,it is required to propose efficient schemes for addressing the problems in the existing literatures.On the other hand,with the increasing of the complexity and scale of the modern control systems,the chances that the systems are subject to faults are also increased.The faults will have an adverse influence on the system and bring a challenge for the security of the system.Therefore,it is necessary to investigate the fault diagnosis problem such that the security of the systems can be guaranteed.Based on the afore-mentioned background,this dissertation further studies the local stabilization and fault diagnosis problem for T-S fuzzy systems.The main purpose in this dissertation is to improve the design.To achieve the above-mentioned purpose,the relationship between the membership functions of the system and those of the controller or observer is fully explored and utilized,then observer and controller design methods are presented and a new research framework is established.The main contents and contributions of this dissertation are outlined as follows:In Chapter 1,the significance and value of this research are emphasized.Meanwhile,the background and the development of the T-S fuzzy systems and fault diagnosis are analyzed and summarized.Additionally,preliminaries are also introduced.In Chapter 2,the local stabilization and tracking control problems for nonGaussian stochastic distribution sampled-data fuzzy systems are investigated.First,the system extension reachable set,the ellipsoid set and the objective area are introduced.Then,by Lyapunov-Krasovskii functionals,a controller strategy is developed.Via the strategy,the relationship among the three above-mentioned sets are established so that the extension reachable set can be contained in the objective area,which guarantees that the objective of local stabilization could be achieved.The strategy establishes a framework so as to facilitate the study of the subsequent chapters.On the other hand,an L? analysis method is proposed to ensure the tracking control performance.Besides,the analysis conditions are given to limit the upper bound of the derivative of the membership functions.Then,the information of the upper bound could be used to design the controller.The asynchronous membership function problem between the system and the controller can be addressed by the proposed method.Moreover,the method removes the requirement in the conventional methods,where the derivative of the membership functions cannot explicitly depend on system input.Finally,the effectiveness of the developed method is verified by a simulation example.In Chapter 3,the local stabilization problem for discrete T-S fuzzy system with sensor fault is studied.First,the case that the system is subject to the sensor fault is fully considered.And the corresponding sensor fault model is obtained and a state feedback controller is constructed.Next,based on Lyapunov-Krasovskii functionals method and the method of free weight matrix,the ellipsoid set for the time-delayed systems is got.Through the ellipsoid set,the extension reachable set is restricted in the objective domain such that the local stability of the system can be ensured.At the same time,in light of the singular values decomposition technology,the coupled matrices are decoupled so that the non-convex problem introduced by the sensor fault can be solved.Besides,a method to estimate the set of the initial conditions is presented.In the proposed method,the influence of the factors,such as the fault and time-delay on the system can be efficiently attenuated so as to guarantee the local stability and the reliability of the system.In the end,an example is given to demonstrate the efficacy of the proposed method.In Chapter 4,the local stabilization problem for T-S fuzzy networked control system with partly immeasurable premise variables is considered.In order to make full use of the information of measurable premise variables,by virtue of the set theory,the system premise variables are divided into two parts(the measurable ones and immeasurable ones)to be described.Then,the measurable premise variables are utilized to construct the controller.By the use of Lyapunov-Krasovskii functionals method,the local stabilization controller design method is given to guarantee the local stability of the system.Second,the delay induced by network is fully considered and the upper bound of deviation between the membership functions of the system and those of the controller is obtained.Then,by employing the information of the upper bound,the problem of the asynchronous membership function can be addressed.The merit of the proposed method lies in that:the information of the system measurable premise variables and the information of the afore-mentioned upper bound can be taken advantage of for improving the design.Finally,the simulation results show the effectiveness of the presented scheme.In Chapter 5,the sensor fault isolation problem for T-S fuzzy systems is addressed.First,a fault isolation scheme with n observers is developed for the system with n sensors.Then,by using the set theory and sufficiently analyzing the influence of the sensor fault on the system premise variables,a scheme about how to select the premise variables of the observer is proposed.Based on the scheme,the information of the sensor can be rightly used to construct the fault isolation observers for an effective fault isolation.Meantime,in order to improve the fault isolation performance,the H_/H? performance index is taken into consideration and the corresponding analysis is made to obtain the fault isolation observer design conditions.Compared with the traditional approaches,the method presented in this chapter can avoid the invalid fault isolation,which is induced by wrongly using the information of the sensor to construct the observer.In the end,the simulation results demonstrate the advantage of the proposed scheme.In Chapter 6,the simultaneously local stabilization and fault detection problem for T-S fuzzy systems is under consideration.First,an observer-based controller is constructed and the corresponding augm ented system is obtained.By means of Lyapunov function method,a local stabilization criterion is proposed,where the local stability of the afore-mentioned augmented system can be ensured.For the purposes of increasing the robustness of the system to the persistent disturbance and the sensitivity of the system to the fault,the L? performance index and finitefrequency H-performance index are introduced.With the above-mentioned indexes,a performance analysis is made to obtain the controller and the observer design conditions.Next,an algorithm is given to solve the parameters of the controller and the observer.The merits of the approach developed in this chapter are that:via the proposed method,the coupled variables in the collaborative design of the local stabilization controller and fault detection observer can be handled such that the multi-objectives can be achieved.Besides,in the proposed approach,the persistent disturbance can be dealt with and the assumption in the H? method,where the disturbance should be energy-bounded,can be removed.Finally,a simulation example verifies the efficacy of the presented method.In the end,the dissertation is concluded and the further research directions are pointed out and discussed.