Research On Synchronous Control Of Fractional Order Chaotic System

As a special form of motion in a nonlinear dynamic system,chaotic motion has great application value in physics,chemistry,biology,and many engineering fields.Chaotic control and chaotic synchronization has became the focus of the discussion on chaotic theory due to as the core of the application to reality.The research of fractional order chaotic system is later than integer order chaotic systems which lacked effective control means.With the development of the application of fractional order chaos theory,the control of fractional order chaotic system will be the challenge we need to face.1.A brief introduction to chaos is introduced.The types of chaotic synchronization and the commonly used methods of chaotic synchronization are summarized.Secondly,the development of fractional calculus,the definition of fractional calculus and its numerical algorithm are also introduced.Finally,the stability related lemmas and theorems of fractional order system are summarized and corresponding proofs are given,which lays a theoretical foundation for subsequent chapters.2.Firstly,the fractional order chaotic system is fuzzed.Secondly,the solution of the fractional differential equation is converted to the solution of the integral order differential equation,the sufficient conditions to satisfy the stability of the error system and the related inference are derived by using parallel distributed compensation method.Finally,designed a state feedback controller based on the sufficient conditions to achieve the self synchronization of fractional order Lorenz system and fractional R?ssler system.3.A new fractional order chaotic system and its dynamic characteristics are introduced.Then,the minimum order of chaos in the fractional order chaotic system is derived and verified by simulation.Finally,the self synchronization of the new fractional order chaotic system is realized by active feedback control and nonlinear observer control.4.The dynamic behaviors of the new fractional order hyperchaos system are introduced.Then,the minimum order of chaos in the fractional order hyperchaos system is explored.Finally,followed by using the active control method,the self synchronization and the nonidentical structure synchronization of the new fractional order hyperchaos system are realized.5.Based on the theory of active control and projective synchronization,a three dimensional fractional order chaotic system and a four dimensional fractional hyperchaotic Lorenz system are taken as an example to design the controller.Then,the dimension reduction synchronization(ROS)and augmented dimension(IOS)synchronization of different dimension fractional order chaotic systems are realized by numerical simulation.Finally,based on the incremental projection synchronization method,the secure communication process of the signal is successfully realized.6.A new pinning adaptive impulsive hybrid synchronization controller was proposed for Chen fractional order complex dynamic network through the generalized Barbalat Lemma.The whole network can be forced to certain desired synchronous state by controlling a part of nodes of the network.The simulation results show that the designed control strategy can effectively achieve the synchronization of fractional order complex dynamic network.Finally,the influence of the number of controlled nodes on the synchronization speed is studied.