Data-based Real-time Solutions And Synchronization Control For Chaotic Systems

As an important branch of nonlinear system,chaotic system has attracted much attention from researchers both at home and abroad since its inception.It has great research value in such fields as atmospheric science,information security,sensing circuit and so on.As a kind of control method to chaotic system,chaos synchronization plays a vital role in the field of secure communication recently.It is of theoretical and engineering significance to research the proper method to realize the synchronization and anti-synchronization between chaotic systems.In this paper,to realize the real-time solving and synchronization control between chaotic systems,we adapt the least squares vector machine(LS-SVM)as the core method.Besides,we do some research on the basic principle and implementation process of LS-SVM,the parameter selection of rolling time window,as well as related simulations.To obtain the real-time approximate solution of the chaotic system,at first,we discretize the time in a time interval and train the model as the sample point of the data.Under the framework of least squares support vector machine,we can get the chaotic system in this time interval.Then,based on the unbiased least squares support vector machine,we can use the discrete value of the approximate solution obtained above to get the approximate solution of the chaotic equation on-line by training the samples in the time window and combining the rolling time window.To realize the mixed synchronization control of the chaotic system,sample the master system to get the number of training samples set,set up hybrid synchronous trajectory form of slave system.At last,we can use the unbiased LS-SVM method to get the optimization target by introducing the kernel function,and obtain the hybrid synchronous trajectory according to the optimization goal.The simulation results show that the proposed method can realize the real-time solution to the chaotic system,and can realize the synchronization and anti-synchronization control of the chaotic system based on the unbiased LS-SVM,besides,the calculation has a high accuracy with a fast speed.