Impulse Response Constrained LS-SVM modeling for Hammerstein System Identification * *EU: The research leading to these results has received funding from the European Research Council under the European Unions Seventh Framework Programme (FP7/2007-2013) / ERC AdG A-DATADRIVE-B (290923). This paper reflects only the authors views and the Union is not liable for any use that may be made of the contained information. Research Council KUL: CoE PFV/10/002 (OPTEC), BIL12/11T; PhD/Postdoc grants Flemish Government: FWO: projects: G.0377.12 (Structured systems), G.088114N (Tensor based data similarity); PhD/Postdoc grant iMinds Medical Information Technologies SBO 2015 IWT: POM II SBO 100031 Belgian Federal Science Policy Office: IUAP P7/19 (DYSCO, Dynamical systems, control and optimization, 2012-2017)

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.