A Recursive Method of Identification of Hammerstein Model Based on Least Squares Support Vector Machines

In the domain of industrial process modeling and control, Hammerstein model has been used widely to describe a class of nonlinear systems. Goethals et al. (2005) proposed a method based on Least Squares Support Vector Machines (LSSVM) to identify the input-output relationship of the Hammerstein model. Unfortunately, as the data points grow, this kernel learning approach costs much time correspondingly. Besides, Goethals’s technique is not suitable for the on-line identification. To this end, a recursive nonlinear identification method is proposed in this paper. The basic idea is to get the recursive form of the parts of the high-dimensional matrix arisen from the optimization derivation, and get the estimation with the trick of sub-inverse matrix. With this new LSSVM approach, the Hammerstein model can be obtained recursively and much quickly, which is crucial to industrial applications that require online estimation and prediction. The simulation illustrates the validity and feasibility of the developed online identification method.