Fuzzy Control And Adaptive Fault Estimation Of Nonlinear Systems

With the development of technology,the practical control systems become more complex,and many systems have the highly nonlinear characterization.Although the nonlinear system theory has been developed in the past decades,due to the complex structure,there still exist many limitations in the practical engineering.Fuzzy logic system as an effective modeling tool,has attracted wide attention from the researchers,which has been the powerful ability of approximating arbitrary smooth nonlinear functions.On the other hand,various types of component failures always occur inevitably in normal operations of practical systems,such as actuator faults and sensor faults.The faults can cause catastrophic accidents,and economic loss.Hence,it is of great importance to develop the fault estimation and fault tolerant control to improve the safety and reliability.In this paper,the superior approximation properties of fuzzy logic system will be employed to develop some fuzzy-model-based robust control and adaptive fuzzy observer design approaches for some kinds of systems.The proposed methods will be used in control and fault estimation problems in continuous stirred tank reactor,the F-404 aircraft engine system,and circuit system.The main research work is summarized as follows:Chapter 2 investigates robust decentralized control problem for a class of continuoustime T-S fuzzy affine large-scale systems which subject to actuator fault and stochastic disturbance.Using state-space partition technique,the global fuzzy model of each subsystem is divided into several piecewise affine fuzzy models,then in each partition region,piecewise affine controllers are designed.Firstly,based on the common Lyapunov function method,combined with the principle of ellipsoid approximation and stochastic system theory,the existence condition of the decentralized piecewise affine controller is obtained.Secondly,by introducing virtual linear systems,nonsingular continuous matrices which satisfy the boundary conditions are constructed to ensure the invertibility of the piecewise Lyapunov matrices.Then,based on the piecewise Lyapunov function method,the existence condition of the decentralized piecewise affine controller is obtained.The proposed new piecewise Lyapunov function constructed method is more advanced than the existing methods,and there is no need to make contraints on controller gains.At the same time,the method based on piecewise Lyapunov function has less conservatism.Chapter 3 investigates output feedback control problem for T-S fuzzy affine systems with unmeasured states in piecewise Lyapunov function methods framework.Firstly,under the assumption that the sensor fault subjects to a Markov process,asynchronous dynamic output feedback control problem is studied.In order to reduce the restricted assumption that each local model has the same input matrix,the integral control input is introduced.Based on the state-space partition technique in Chapter 2,piecewise fuzzy affine observer and piecewise affine controller are designed in each divided region.Then a new augmented closed-loop system is established whose states include the original states,the error variables,and the control input.The asynchronous problem of the states trajectories between the plant and the observer,that is,they may appear in different regions at the same time.The sufficient conditions are obtained to guarantee the asymptotic stability of error system and the robust performance.The result obtained is more advanced because it adapt to the case that the precise variables are unmeasured and the dynamic decoupling method can be extended to uncertain fuzzy systems to realize the decouple between the uncertainties and the control input.Secondly,considering the controller gain variations,fragile static output feedback control problem is studied.To avoid the tedious calculation process to solve the inverse matrices of piecewise Lyapunov matrices,this part develops two new methods to design controllers,the first one based on the constraint condition on input matrix and the second one based on state-input augmented.The latter one realizes the decouple between input matrices and the control matrices,and reduces the assumption that the input matrices are need to be full column rank,thus the results obtained are less conservatism than the existing results.In the above two chapters,the bound of the faults or parameter perturbations is required to be available.However,in the practical engineering,the prior knowledge of the faults is difficult to obtain.The fault estimation observer can estimate the size and shape of faults,which is an important step in the active fault-tolerant control.For the fault estimation problem in switched nonlinear systems,most of the existing results are based on the sliding mode observer approach.However,since the mode-dependent characterization of the sliding surface leads to the switching problem of the sliding surface,it is difficult to guarantee the strict reachability of the sliding surface.In addition,the nonlinear functions in the existing results are usually required to satisfy the Lipschitz condition with known or unknown Lipschitz constant.Chapter 4 investigates the adaptive fuzzy fault estimation problem for Markovian jump nonlinear systems with sensor faults.The bound of the sensor faults and the nonlinear functions is unknown,where the unknown nonlinearity is approximated by the fuzzy logic systems.By the system augmented technique,the original states and sensor faults are combined into the extended state vector.Then,introducing the linear transformation,a new adaptive fuzzy observer approach has been developed,and the precise estimation of the state and sensor fault can be obtained.Chapter 5 investigates the fault estimation problem for switched nonlinear systems with actuator faults,sensor faults,and unknown nonlinearities.By the linear transformation,the original switched systems can be transformed into two subsystems to achieve the decoupling of the actuator faults and sensor faults.Based on the decoupling models,two adaptive fuzzy switched observers have been designed to estimate the actuator and sensor faults,and the nonlinear functions are approximated by the fuzzy logic systems.It is noted that,by introducing a measurable signal generated by the outputs,the sensor faults can be transformed into the form of actuator faults,which makes the fault estimation design process simple and precise.