Research And Application Of Finite-time Synchronization For Fractional-order Nonlinear Systems

Fractional calculus is a theory developed from the mathematical background of integral and differential of integer order.It is a more accurate mathematical modeling method,which can describe the dynamic process of various control systems in the world in detail.Therefore,it has attracted much attention from scholars.Chaotic system,as one of the nonlinear systems,is characterized by high complexity,sensitivity to initial values and unpredictable randomness.It also has the advantage of clearly expressing the physical meaning of the system,and has been applied by many researchers in the fields of meteorology,geology,finance and so on.Synchronization is a common group phenomenon in nonlinear systems.A variety of synchronization control methods for fractional-order chaotic systems have become a hot topic in recent years.But many synchronization methods are discussed in infinite-time domain,with the deepening of research,it has become one of the hot research directions in recent years that the control system can reach a stable state in finite-time.At present,most of the research on finite-time synchronization focuses on integer-order systems,so the research on finite-time synchronization of fractional-order nonlinear systems is a topic of great research significance.Under the support of fractional-order calculus theory,Lyapunov stability theory,finite-time stability theory and unknown parameters identification method,this paper carries out research on finite-time synchronization of multiple fractional-order chaotic systems.The main research contents are as follows:Firstly,the finite time synchronization of fractional order chaotic systems with different orders is discussed.First,the finite time stability theorem of fractional order chaotic system is derived again,and a new expression is obtained.Then,the chaotic behavior of fractional-order system with equal order is analyzed,and a finite-time controller is designed to make the error system converge quickly in finite-time.Then,the system of the same order is extended to the system of different orders.By using the basic properties of fractional calculus,the low order system is transformed into a problem of the same order which can be discussed by using the ascending order method,and then the corresponding new finite-time controller is constructed by combining with the finite-time stability theory,so that the master-slave system can achieve finite-time synchronization.Secondly,considering the existence of external disturbances,the finite-time synchronization problem of fractional-order hyperchaotic systems with different structures is studied.In this paper,two kinds of systems without disturbance and with disturbance are compared and analyzed.Based on the finite-time Lyapunov stability theory,a finite-time controller is designed according to the characteristics of the controlled system without disturbance,which achieves the effect of synchronous tracking of various variables in the system in a finite-time.When there is disturbance in the system,a finite-time controller that can suppress the disturbance is constructed,which successfully weakens the influence of the disturbance on the system,and ensures the convergence of the synchronization error in a finite-time,and realize the finite-time synchronization of fractional-order hyperchaotic system with disturbance.Finally,the parameter identification rules and the finite-time synchronization method are applied to the fractional-order model of PMSM.When the parameters of PMSM system are in a certain range,the system performance will decrease due to the appearance of chaotic behavior.At the same time,in order to ensure that the controlled system will not be affected by unknown items,a finite-time controller is designed for this phenomenon,and the parameter identification rules are introduced into it,so that the state variables of the motor system could quickly converge to the equilibrium point in a finite-time.Theoretical derivation and numerical simulation verify that the proposed scheme can be successfully combined with PMSM.