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Set membership estimation by weighted least squares support vector machines

CHAI Wei1,2,SUN Xian-fang1 (1.School of Automation Science and Electrical Engineering,Beihang University,Beijing 100191,China;2.School of Electronics Information and Control Engineering,Beijing University of Technology,Beijing 100124,China)  
A set membership estimation method by weighted least squares support vector machines(LS-SVM) was proposed for nonlinear-in-parameter regression models with unknown but bounded errors.A weighted least squares support vector regression(LS-SVR) was solved to build a model which approximated the complex functional relationship between the weighted l∞ norms of the equation-error vectors and the given parameter vectors.Then the approximate feasible parameter set was obtained according to this model and the feasible weighted l∞ norms of the equation-error vectors.In order to evaluate the results of the proposed method,an index reflecting the closeness between the approximate boundary and the true boundary was given.The simulation results show that the proposed method can give approximate boundaries much closer to true boundaries than the method by unweighted LS-SVM.
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