Identification of Nonlinear Systems Using Multi-scale Wavelet Support Vectors Machines

New identification method of non-linear dynamic systems based on multi-scale wavelet least squares support vector machines (MS-LS-SVM) is proposed. Support vector machines (SVM) is a novel machine learning method based on small-sample statistical learning theory, which is powerful to deal with small sample, nonlinearity, high dimension, and local minima. Least squares support vector machines (LS-SVM) is an updating SVM version which involve equality instead of inequality constraints of standard SVM to simplify the process of SVM. Wavelet function with different resolution is used as kernel function in order to construct MS-LS-SVM. The condition of support vector kernel function is proved. This kind of kernel function can simulate almost any function in quadratic integral space, so it enhances the generalization ability of the SVM. According to the multi-scale wavelet kernel function and regularization theory, MS-LS-SVM regression model is proposed. The regression model formulates a new identification method of non-linear systems. Experiments show the proposed method not only has better identification precision, but also improves robustness and generalization than neural networks.