Identification of MIMO Hammerstein models using least squares support vector machines

This paper studies a method for the identification of Hammerstein models based on least squares support vector machines (LS-SVMs). The technique allows for the determination of the memoryless static nonlinearity as well as the estimation of the model parameters of the dynamic ARX part. This is done by applying the equivalent of Bai's overparameterization method for identification of Hammerstein systems in an LS-SVM context. The SISO as well as the MIMO identification cases are elaborated. The technique can lead to significant improvements with respect to classical overparameterization methods as illustrated in a number of examples. Another important advantage is that no stringent assumptions on the nature of the nonlinearity need to be imposed except for a certain degree of smoothness.