Research On Fractional-order Chaotic System With Different Structure And Its Synchronization Control

Chaos is ubiquitous in nature,and more and more fields have found chaos phenomenon,the application of chaos control to physical systems is the ultimate trend of the development of chaos.Fractional calculus theory has been studied for more than 300 years,but its application in engineering and physics has become a hot topic in recent decades.Fractional order chaos theory,as a new research direction,will become an important part of nonlinear science.Due to the existence of fractional order chaotic systems with different structure,it is significant to study the control and synchronization of fractional order chaotic systems with different structure.After understanding the basic theory of fractional chaos,this paper analyzes and studies the regional pole assignment problem of integer order and fractional order system.According to the stability condition of integer order system,the stability condition of fractional order system is deduced.Some criteria are proposed to ensure the pole assignment of fractional order system in the specified region,and the state feedback controller is designed to achieve the goal of system stability.Finally,we use the LMI toolbox for numerical simulation validation.In order to extend the research of fractional linear system to fractional order nonlinear system,this paper study the chaotic synchronization problem of fractional order of different structure.In this paper,the fuzzy control and sliding mode control method are used to design the appropriate sliding mode and fuzzy rules.According to the existing fractional stability theory,the synchronization control of fractional chaotic systems with two different structures is realized.The simulation results prove the correctness and practicability of the design method.