Applying Of The Fuzzy Logic System In Fractional-order Chaotic Systems With Different Structures

Adaptive fuzzy system is one of the most effective mathematical methods for the synchronization of fractional-order chaotic systems.Owing to effect of uncertain term,external disturbance,time-delay and so on in fractional-order chaotic systems,the synchronization of fractional-order chaotic systems with different structures is not easy.Therefore,in order to achieve the synchronization for fractional-order chaotic systems with different structures,the main work is to induce effect of these unknown terms.The paper designs the adaptation law and the corresponding controller.On one hand,it solves the synchronization of fractional-order chaotic systems with different structures by the way of combining the fuzzy logic system with backstepping control.On the other hand,this paper also achieves the synchronization for fractional-order chaotic systems with different structures via designing adaptive fuzzy logic systems.This paper contains three chapters,the details are as follows:Chapter 1:Preliminaries.This chapter introduces conception of fractional calculus and some basic conclusions,and construction,form and theorem about the fuzzy logic system.Chapter 2:Adaptive fuzzy backstepping control of two classes of uncertain fractional-order chaotic systems with external disturbances.Firstly,the chapter gives two classes of uncertain fractional-order chaotic systems,and describes the question needed to be solved.Secondly,we introduce controller design and stability analysis to achieve the synchronization of fractional-order chaotic systems.Finally,numerical simulation is displayed and tests better effectiveness of the designed controller.Chapter 3:Adaptive fuzzy synchronization of uncertain fractional-order chaotic systems with different structures and time-delays.First of all,we introduce two classes of unknown fractional-order chaotic systems with time-delays.Next,we discuss corresponding conclusions and design controller.In the final,numerical simulation is shown and proves that the designed method has good effectiveness.