{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:31:50Z","timestamp":1787322710462,"version":"build-2736575974"},"reference-count":27,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2015,1]]},"abstract":"<jats:p>In this paper, we study the problem of identifying the impulse response of a linear time invariant (LTI) dynamical system from the knowledge of the input signal and a finite set of noisy output observations. We adopt an approach based on regularization in a reproducing kernel Hilbert space (RKHS) that takes into account both continuous- and discrete-time systems. The focus of the paper is on designing spaces that are well suited for temporal impulse response modeling. To this end, we construct and characterize general families of kernels that incorporate system properties such as stability, relative degree, absence of oscillatory behavior, smoothness, or delay. In addition, we discuss the possibility of automatically searching over these classes by means of kernel learning techniques, so as to capture different modes of the system to be identified.<\/jats:p>","DOI":"10.1137\/130920319","type":"journal-article","created":{"date-parts":[[2015,10,27]],"date-time":"2015-10-27T12:24:04Z","timestamp":1445948644000},"page":"3299-3317","source":"Crossref","is-referenced-by-count":63,"title":["Kernels for Linear Time Invariant System Identification"],"prefix":"10.1137","volume":"53","author":[{"given":"Francesco","family":"Dinuzzo","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2015,10,27]]},"reference":[{"key":"atypb1","unstructured":"L. Ljung,\n                      System Identification: Theory for the User\n                      , 2nd ed., Prentice-Hall, Englewood Cliffs, NJ, 1999."},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1137\/090755436"},{"key":"atypb3","first-page":"2953","author":"Mohan K.","year":"2010","journal-title":"NJ"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2009.10.031"},{"key":"atypb5","doi-asserted-by":"crossref","unstructured":"C. E. Rasmussen and C. K. I. Williams,\n                      Gaussian Processes for Machine Learning\n                      , MIT Press, Cambridge, MA, 2006.","DOI":"10.7551\/mitpress\/3206.001.0001"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2012.05.026"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2014.01.001"},{"key":"atypb8","unstructured":"A. N. Tikhonov and V. Y. Arsenin,\n                      Solutions of Ill Posed Problems\n                      , W. H. Winston, Washington, 1977."},{"key":"atypb9","doi-asserted-by":"crossref","unstructured":"G. Wahba,\n                      Spline Models for Observational Data\n                      , CBMS-NSF Regional Conf. Ser. in Appl. Math. 59, SIAM, Philadelphia, 1990.","DOI":"10.1137\/1.9781611970128"},{"key":"atypb10","doi-asserted-by":"crossref","unstructured":"F. R. Bach, G. R. G. Lanckriet, and M. I. Jordan,\n                      Multiple kernel learning, conic duality, and the SMO algorithm\n                      , in Proceedings of the Twenty-first International Conference on Machine Learning, ACM, New York, 2004, pp. 6ff.","DOI":"10.1145\/1015330.1015424"},{"key":"atypb11","first-page":"1099","volume":"6","author":"Micchelli C. A.","year":"2005","journal-title":"J. Mach. Learning Res."},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(71)90184-3"},{"key":"atypb13","first-page":"189","author":"Dinuzzo F.","year":"2012","journal-title":"MA"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1950-0051437-7"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1109\/9.948469"},{"key":"atypb16","doi-asserted-by":"crossref","unstructured":"S. Siddiqi, B. Boots, and G. J. Gordon,\n                      A constraint generation approach to learning stable linear dynamical systems\n                      , in Proceedings of the Conference on Advances in Neural Information Processing Systems, Vancouver, Canada, 2008.","DOI":"10.21236\/ADA480921"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1142\/S0219530506000838"},{"key":"atypb18","doi-asserted-by":"crossref","unstructured":"I. Steinwart and A. Christmann,\n                      Support Vector Machines\n                      , Springer, New York, 2008.","DOI":"10.1007\/978-0-387-77242-4"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1007\/BF00276494"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1007\/BF02592679"},{"key":"atypb21","unstructured":"D. Widder,\n                      The Laplace Transform\n                      , Princeton University Press, Princeton, NJ, 1941."},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.2307\/1968466"},{"key":"atypb23","first-page":"338","author":"Argyriou A.","year":"2005","journal-title":"Heidelberg"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1007\/BF01404567"},{"key":"atypb25","first-page":"211","volume":"1","author":"Tipping M.","year":"2001","journal-title":"J. Mach. Learning Res."},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2014.2351851"},{"key":"atypb27","unstructured":"F. Dinuzzo,\n                      Kernel Machines with Two Layers and Multiple Kernel Learning\n                      , preprint, http:\/\/arxiv.org\/abs\/1001.2909arXiv:1001.2909, 2010."}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/130920319","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:24:35Z","timestamp":1787318675000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/130920319"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,1]]},"references-count":27,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2015,1]]}},"alternative-id":["10.1137\/130920319"],"URL":"https:\/\/doi.org\/10.1137\/130920319","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,1]]}}}