Fault Estimation For T-S Fuzzy Systems With Asynchronous Membership Functions

Generally speaking,the practical engineering systems are almost nonlinear systems,it is very meaningful to study the nonlinear systems.The Takagi-Sugeno(T-S)fuzzy model is an effective method for approximating nonlinearity and has been widely applied to practical industries.With the increasing scale and complexity of modern industrial systems,failures are always inevitable,and they will seriously affect the performance of the systems.Moreover,the requirements for the security and reliability of systems are increasing in the industry.Therefore,fault estimation problem has received extensive attention.At the same time,the T-S model with asynchronous membership functions can represent a wider range of nonlinear systems.Thus,this thesis studies the fault estimation problem for T-S fuzzy systems with asynchronous membership functions.The main contents of this thesis are as follows:Firstly,the fault estimation problem is investigated for the T-S system with unmeasurable premise variables.Different from the existing adaptive fault estimation scheme,premise variables in this thesis are unmeasurable.Therefore,the membership function between the system and the observer is asynchronous,which makes the parallel distributed compensation(PDC)-based fault estimation strategies being infeasible.In this case,the fuzzy adaptive observer is designed.In addition,with the help of the Lyapunov method and linear matrix inequality(LMI)technique,sufficient design conditions of observer can be obtained.At the same time,it can be proved that the estimation errors of system state and fault parameters are uniformly bounded.In particular,the considered reference signals are injected directly in the controller to excite the system states to ensure persistent excitation(PE)condition.Secondly,this thesis is concerned with the event-triggered adaptive fault estimation problem for T-S fuzzy systems with actuator faults and external disturbances.Due to the existence of event-triggered communication(ETC)mechanism,the fuzzy systems and adaptive fault estimation observers cannot share the same premise variables,which makes the problem of asynchronous membership function.In order to overcome this difficulty,the deviation information of the membership functions between the systems and the observers is injected into the ETC condition.Under this framework,an event-triggered adaptive observer is then designed to jointly estimate the system states and fault parameters.Moreover,it is proved that the estimation errors are uniformly bounded and the network resources are also saved.Especially,via the linear matrix inequality(LMI)-based optimization technique,the bounds of the estimation errors are minimized.Finally,for the considered two class of fault estimation systems,two examples are given to illustrate the feasibility and effectiveness of the proposed adaptive observer methods.