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In some nonlinear dynamic systems,the state variables function usually can be separated from the control variables function,which brings much trouble to the identifcation of such systems.To well solve this problem,an improved least squares support vector regression(LSSVR)model with multiple-kernel is proposed and the model is applied to the nonlinear separable system identifcation.This method utilizes the excellent nonlinear mapping ability of Morlet wavelet kernel function and combines the state and control variables information into a kernel matrix.Using the composite wavelet kernel,the LSSVR includes two nonlinear functions,whose variables are the state variables and the control ones respectively,in this way,the regression function can gain better nonlinear mapping ability,and it can simulate almost any curve in quadratic continuous integral space.Then,they are used to identify the two functions in the separable nonlinear dynamic system.Simulation results show that the multiple-kernel LSSVR method can greatly improve the identifcation accuracy than the single kernel method,and the Morlet wavelet kernel is more effcient than the other kernels.
In some nonlinear dynamic systems, the state variables function usually can be separated from the control variables function, which brings much trouble to the identifcation of such systems. To solve this problem, an improved least squares support vector regression (LSSVR) model with multiple -kernel is proposed and the model is applied to the nonlinear separable system identifcation. This method utilizes the excellent nonlinear mapping ability of Morlet wavelet kernel function and combines the state and control variables information into a kernel matrix. Using the composite wavelet kernel, the LSSVR includes two nonlinear functions, whose variables are the state variables and the control ones respectively, in this way, the regression function can gain better nonlinear mapping ability, and it can simulate almost any curve in quadratic continuous integral space.Then, they are used to identify the two functions in the separable nonlinear dynamic system. Simulation results show that the multiple-kern el LSSVR method can greatly improve the identifcation accuracy than the single kernel method, and the Morlet wavelet kernel is more effcient than the other kernels.