Offline modeling of nonlinear systems based on least squares support vector machines

Least squares support vector machines (LS-SVM) based on a group of different kernel functions (Linear-Polynomial-Radial Basis Function- Exponential Radial Basis Function) for modeling nonlinear systems is introduced in this paper. A method for selecting the hyperparameters of LS-SVM is presented in details for both the regularization parameter (¿) and the width parameter (¿). To test the validity of the LS-SVM method, this paper demonstrates that the method introduced can be used effectively for the identification of nonlinear systems. Simulation results reveals that the Polynomial kernel function obtain the best performance in comparison to other kernel functions especially RBF which is the most common one in modeling nonlinear systems. LS-SVM with the proposed method for parameter selection provides an attractive approach to study the properties of complex nonlinear system modeling.