Impulse Response Constrained LS-SVM modeling for Hammerstein System Identification

Abstract

Hammerstein systems are composed by a static nonlinearity followed by a linear dynamic system. The proposed method for identifying Hammerstein systems consists of a formulation within the Least Squares Support Vector Machines (LS-SVM) framework where the Impulse Response of the system is incorporated as a constraint. A fundamental aspect of this work is that the structure of the Hammerstein system allows to obtain an impulse response that approximates the linear block while LS-SVM models the nonlinearity. When the resulting model is trained, the regularization capabilities of LS-SVM are applied to the whole model. One of the main advantages of this method comes from the fact that while it incorporates information about the structure of the system, the solution of the model still follows from a simple linear system of equations. The performance of the proposed methodology is shown through two simulation examples and for different hyper-parameter tuning techniques.