Research On The Synchronization Of Fractional Order Chaotic Systems Based On RBF Neural Network Control

With the progress of communication technology and the influence of chaos science deeply into all kinds of disciplines,fractional calculus theory solves the problem that integer order theory can not solve,and fractional order chaotic system and fractional order control have been paid much attention.Fractional-order chaotic system have been widely used in image encryption,bioengineering,physics,and other fields,which have achieved challenging results due to the good flexibility,robustness,high accuracy.The research on Synchronization problems of systems,the integer order system synchronization is mainly researched,but it's few studies for fractional order system synchronization.Because the traditional integer order system has not met the high complexity,easy implementation and so on in the field of engineering,the synchronization control of the fractional order chaotic systems research has been more and more important.At present,there are many ways such as sliding mode control,soft control,fuzzy control and so on in view of the fractional order chaotic systems synchronization.Among the many methods,RBF neural network control stands out because of its strong self-anti-interference,which makes the system has strong robustness and can be well combined with other control methods,making the RBF neural network controller has good flexibility,accuracy,and realization.Based on fractional calculus theory,Lyapunov stability theory,finite time control,sliding mode and PMSM theory,RBF neural network parameter self-interference theory,and state observer theory,firstly,RBF adaptive control for fractional-order hyperchaotic systems with time delay is proposed.Then,the finite time synchronization of the hyperchaotic system with unknown internal parameters and external disturbances is realized based on RBF neural network controller.Finally,the RBF controller is applied to the permanent magnet synchronous motor to control the rotor speed of the motor.The main contents are as follows:Firstly,the research situation of fractional-order chaotic systems at home and abroad is introduced,of which the fractional-order chaotic systems,fractional-order synchronization control and RBF neural network control are introduced in detail.It provides a realistic background for the application of RBF neural network in the synchronization of fraction-order hyper-chaos system and permanent magnet synchronous motor system.Then,the theory of fractional calculus,including the definition of calculus,properties,synchronization control method are introduced,and the development process,basic principle and design strategy of RBF neural network control are highlighted,which provides a solid theoretical basis for the study of this paper.Secondly,a controller with integer order adaptive rate of RBF neural network is designed for a class of time-varying synchronization control problems with disturbances,which solves the problems of time delay and external interference of fractional-order hyper-chaotic systems,and finally the drive system can follow the slave system completely.The MATLAB numerical simulation results show that the controller is effective,feasible and robust,and can realize synchronization of fraction-order hyper-chaotic system Chen system.Then,the synchronization of two different fractional order systems is designed based on RBF neural network.Firstly,an effective RBF neural network controller is designed for the same structure fractional order system,which realizes the complete synchronization of the same structure fractional order system.Secondly,as for the finite time synchronization control problem of hyperchaotic systems with different structures and disturbances,RBF neural network control strategy and state observer strategy are designed to eliminate internal uncertainties and external disturbances,and a new type of adaptive sliding mode surface is proposed Based on the finite-time stability theory and Lyapunov stability theory,a robust finite-time sliding mode controller is proposed.By changing the parameters in the controller and introducing RBF neural network control,the fractional-order chaotic system with uncertain external interference can finally realize the sliding mode synchronization control of the finite-time fractional-order hyper-chaotic system.A novel adaptive sliding mode is proposed to synchronize the systems.The results of MATLAB numerical simulation show that the designed controller can achieve synchronization in a limited time,which is effective and feasible.Finally,the sliding mode control and RBF neural network control of PMSM are applied in the speed control of permanent magnet synchronous motor respectively.Firstly,the sliding mode dynamic compensation is designed for the uncertainties of permanent magnet synchronous motor,which is verified is effective and feasible for the actual system.Then the fractional RBF controller is applied in the speed control of permanent magnet synchronous system to improve the robustness of the system and reduce chattering.The simulation results of MATLAB verify that the designed controller is practical and feasible.