Regularized linear system identification using atomic, nuclear and kernel-based norms: The role of the stability constraint

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• 作者：Gianluigi Pillonetto^a ; ¹ ; ^{giapi@dei.unipd.it" class="auth_mail" title="E-mail the corresponding author}Author Vitae ; Tianshi Chen^b ; ^{tschen@isy.liu.se" class="auth_mail" title="E-mail the corresponding author}Author Vitae ; Alessandro Chiuso^a ; ^{chiuso@dei.unipd.it" class="auth_mail" title="E-mail the corresponding author}Author Vitae ; Giuseppe De Nicolao^c ; ^{giuseppe.denicolao@unipv.it" class="auth_mail" title="E-mail the corresponding author}Author Vitae ; Lennart Ljung^b ; ^{ljung@isy.liu.se" class="auth_mail" title="E-mail the corresponding author}Author Vitae
• 关键词：Linear system identification ; Kernel-based regularization ; Atomic and nuclear norms ; Hankel operator ; Lasso ; Bayesian interpretation of regularization ; Gaussian processes ; Reproducing kernel Hilbert spaces
• 刊名：Automatica
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：69
• 期：Complete
• 页码：137-149
• 全文大小：879 K

文摘

Inspired by ideas taken from the machine learning literature, new regularization techniques have been recently introduced in linear system identification. In particular, all the adopted estimators solve a regularized least squares problem, differing in the nature of the penalty term assigned to the impulse response. Popular choices include atomic and nuclear norms (applied to Hankel matrices) as well as norms induced by the so called stable spline kernels. In this paper, a comparative study of estimators based on these different types of regularizers is reported. Our findings reveal that stable spline kernels outperform approaches based on atomic and nuclear norms since they suitably embed information on impulse response stability and smoothness. This point is illustrated using the Bayesian interpretation of regularization. We also design a new class of regularizers defined by “integral” versions of stable spline/TC kernels. Under quite realistic experimental conditions, the new estimators outperform classical prediction error methods also when the latter are equipped with an oracle for model order selection.