Support Vector Machine Identification of Subspace Hammerstein Models

Abstract

Abstract — In this work a new method for identifying subspace Hammerstein systems based on Support vector machine regression is presented. It has been developed by modifying a least-square support vector machine based approach presented earlier. The new algorithm exploits the properties of generic SVM which LS-SVM based algorithm lacks. These properties are robustness in the presence of outliers and sparseness of solution. The proposed algorithm is reduced to include the least number of quadratic programming problems needed to estimate the system matrices and nonlinearity which in turn will reduce the computation complexity of the algorithm. Index Terms — Hammerstein models, subspace identification, support vector machines. I. I NTRODUCTION For researchers and practitioners, modeling is an essential instrument to realize and improve system dynamics [1]. In physical modeling, similarity is used to simulate the real system. For example, an analog computer may be used to build something that behaves almost like the original system. However, to model a complicated engineering system, one must use different method, such as pure mathematical representation, as an analog computer representation would be huge and complicated [2]. Such mathematical representations can be found from fundamental principles, for instance: Newton’s laws, Kirchhoff’s laws, conservation laws, etc. However, this approach is inappropriate for complicated systems [3]. System identification, which is the science of deriving mathematical procedures that form a suitable mathematical model of a system from available input and output data, is good modeling candidate for complex systems. It has caught the attention of researchers and practitioners for many years [4], [5]. In the last two decades, subspace identification theory [6], [7] has attracted researchers’ interest because of its efficiency in identifying state-space models for high order, multiple input, multiple