Adaptive Fuzzy Backstepping Control For Fractional-Order Nonlinear Systems

In real life,nonlinear systems generally have system uncertainties,such as un-known external disturbances,inaccuracies in system modeling,system parameter un-certainties and so on.Because the uncertainty of nonlinear systems will affect the control performance of the system,it is of great theoretical value and practical sig-nificance to study the control problem of nonlinear systems.Adaptive fuzzy control is an effective tool for the control of uncertain nonlinear systems.Moreover,back-stepping control method is an effective tool to solve the control problem of a class of nonlinear systems with strict.feedback form.The standard backstepping control is a recursive control algorithm.In this control algorithm,a virtual controller is de-signed for each subsystem of the integer-order nonlinear system in strict feedback form,and the analytical calculation of its partial derivatives is required.However,in the fractional-order nonlinear system with strict feedback form,the virtual controllers are usually designed by composite functions,and their fractional-order derivatives have complex forms.Because of this,there are few literature considering the backstepping control method for fractional-order nonlinear systems with strict feedback.Based on the method of adaptive fuzzy backstepping control and the theory of fractional-order Lyapunov stability,in this thesis,we study the adaptive fuzzy backstepping control for a class of fractional-order nonlinear systems with strict feedback form.Further-more,for the inherent explosion of complexity problem in the standard backstepping control method,further research is carried out,theoretical proof of system stability is presented,and numerical simulation results are also given.The main works of this thesis is as follows:Firstly,the control problem of fractional-order chaotic systems with input satu-ration and unknown external disturbance is studied by adaptive fuzzy backstepping control method.In this thesis,a function that exceeds the saturation amplitude is taken as part of unknown function,and it is approximated by fuzzy logic system in every step.In the process of extending the backstepping control method to the fractional-order chaotic system,the fractional-order derivative of the virtual control function and the unknown function of the system are approximated by fuzzy system.Based on this method,we can avoid the inherent complexity problem in the standard backstepping control method.This method is a generalization of backstepping control for integer-order nonlinear systems.Secondly,based on the work of the first part,an adaptive fuzzy synchronization controller is designed for fractional-order chaotic systems with input saturation and unknown external disturbance based on the backstepping control method.Based on the fractional-order Lyapunov stability theory and adaptive fuzzy backstepping con-trol,the fractional-order adaptation laws and synchronization controller are designed.The adjustable parameters of the system are updated by the fractional-order adapta-tion laws.The fractional-order adaptation law of fuzzy system parameters has higher degrees of freedom than that of integer-order adaptation law.We study the synchro-nization error of the drive system and the response system which are the same class of fractional-order chaotic system,and the response system is a fractional-order chaotic system with input saturation and unknown disturbance in this thesis.Under the de-signed synchronization controller and the fractional-order Lyapunov stability theory,the output variable of the synchronization error system asymptotically approaches to zero within a short time,that is,the response system can be synchronously traced to the drive system rapidly.Thirdly,based on the methods studied in the first two parts,we further study the problem of adaptive fuzzy control based on command filter for a class of fractional-order nonlinear systems.In this thesis,the command filter in integer-order nonlinear systems is successfully extended to fractional-order nonlinear systems,the fractional-order command filter is designed.Therefore,when we discuss the adaptive fuzzy backstepping control problem of fractional-order nonlinear systems,we can not only use fuzzy logic system to approximate the fractional-order derivative of virtual con-troller,but also use the method of command filter to avoid the inherent explosion of the complexity problem in the traditional backstepping control scheme.This gives a further impetus to the study of adaptive fuzzy backstepping control for fractional-order nonlinear systems.Forthly,based on the work of the third part,we study the problem of adap-tive fuzzy synchronization control of fractional-order chaotic systems based on the backstepping control method of fractional-order command filter and the theory of fractional-order Lyapunov stability theory.The fractional-order drive chaotic system and the fractional-order response chaotic system are discussed in this thesis that are the same type of fractional-order chaotic system.In order to eliminate the errors are caused by the operation of command filter,we design the compensation error mecha-nism,and numerical simulation results illustrate the effectiveness of the method.