Research On Finite-time Synchronization Of Fractional-order Chaotic Systems At Preset Time

Fractional-order chaos has fractional-order operation and high degree of nonlinearity,which presents more complex behavior than integer-order chaos.However,the finite time synchronization of fractional-order chaos often has the following problems in practical application.First of all,due to the inevitable errors on the physical plane,the internal uncertainty of the controlled object exists.Secondly,the actual production process often has a large number of interference factors.Finally,most fractional-order chaotic systems cannot complete synchronization at a certain time point.Aiming at the above problems,this paper combines the characteristics of fractional-order chaotic systems,adaptive control theory,sliding mode control theory,"Super-Twisting" control law,finite-time control theory and fuzzy control methods,and designs for different types of fractional-order chaotic systems.The controller is synchronized with a limited time,and its stability is analyzed.First,for fractional-order chaotic systems with different structures that contain internal uncertainties and external disturbances,a finite time projection synchronization with an adaptive law is designed to make it possible to estimate unknown parameters,thereby greatly improving the stability and adaptability of the system.At the same time,a new sliding mode surface is adopted to make the system situated on the sliding mode surface in the initial stage,thereby eliminating the process of reaching the sliding mode surface in sliding mode control,and greatly improving the robustness of the system.In addition,the design of the controller also enables synchronization to be completed in a preset time,which is more practical in practical applications.Secondly,although sliding mode control has obvious advantages in robustness,the use of the sign function in the controller makes the output of the controller discontinuous,which leads to chattering.This will greatly reduce the service life of the machine in practical applications.In order to solve this problem,two ideas are used.One is to add the fuzzy control method to the structure of the sliding mode control,and the other is to use the "Super-Twisting" control law to improve the traditional sliding mode control.Thereby reducing the amplitude and frequency of chattering.The experimental results show that for the synchronization of different-dimensional fractional-order chaotic systems,synchronization can be achieved at a preset time point while ensuring that the system can adapt to unknown disturbances and external disturbances.And the maximum amplitude,average amplitude and vibration frequency of controller chattering have been significantly reduced.Finally,for the finite time bounded synchronization of the fractional-order chaotic system,and the response system has external interference and internal uncertainty.Fractional disturbance observer is introduced into the finite time sliding mode controller,and the ability of disturbance observer to approximate the external disturbance function is used to offset the external disturbance and internal uncertainty.The discontinuity of the controller is weakened,and the burden on the output of the controller is reduced.With the error within a certain range,the limited time synchronization is realized at the preset time.