Research On Control Methods Of Synchronization Of Fractional Chaotic Systems

Chaos is an important component of nonlinear science,which describes complex and irregular motions.Chaotic systems have the characteristics of randomness,initial value sensitivity,and irregularity.Therefore,it is widely used in various fields such as communication,bioengineering,physics,economic modeling,and so on.Due to continuous exploration of chaotic systems,the order of chaotic systems has been extended from integer to fractional order,and a fractional order chaotic system model has been obtained.The dynamic characteristics presented by this model are rather more complex.Chaos synchronization,as an important research direction in the field of chaos,has received widespread attention since it was first proposed.It refers to controlling two or more chaotic systems to asymptotically converge on their state trajectories or achieve consistency in a finite time.Due to the application advantages of fractional order chaotic synchronization in image encryption and secure communication,it is of great practical significance to study the synchronization control methods for fractional order chaotic systems.The content and research results discussed in this article are as follows:1.Study the synchronization of incommensurate fractional unified chaotic systems with unknown disturbances.To solve unknown disturbances,a new fractional order disturbance observer is proposed to estimate the external disturbances of unified chaotic systems.By using an integral sliding mode surface and combining the designed fractional order disturbance observer with an adaptive law,a synchronization controller is designed to achieve two incommensurate fractional order unified chaotic systems with different initial conditions.Theoretical proof and synchronous simulation verify the effectiveness of the designed controller.2.The finite time synchronization problem of incommensurate fractional order chaotic systems with unknown disturbances and uncertainties under different initial conditions is discussed.To deal with unknown disturbances and uncertainties in systems,a new fractional order finite time disturbance observer is designed based on fractional order finite time synchronization theory to estimate external unknown disturbances and uncertainties.Combining a fractional order finite time disturbance observer,a finite time synchronization controller was designed to ensure that the motion trajectory of the system can converge in finite time under different initial conditions.The effectiveness of this controller has been theoretically proven.The numerical simulation using MATLAB futher proves that the designed fractional order disturbance observer and controller are effective and feasible.3.Propose a heterogeneous synchronization controller for different fractional order chaotic systems.Firstly,based on fractional order stability theory,an active synchronization controller is designed,under which the fractional order heterogeneous structure system achieves asymptotic synchronization;Secondly,based on fractional order finite time theory and fractional order stability theory,a finite time synchronization controller is designed to make the motion trajectories of different fractional order chaotic systems tend to be consistent in finite time.The mathematical proof process and simulation results are given to prove the effectiveness of the two different controllers.