A new kernel-based approach to overparameterized Hammerstein system identification

R.S. Risuleo, G. Bottegal, H. Hjalmarsson

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

8 Citations (Scopus)


IThe object of this paper is the identification of Hammerstein systems, which are dynamic systems consisting of a static nonlinearity and a linear time-invariant dynamic system in cascade. We assume that the nonlinear function can be described as a linear combination of p basis functions. We model the system dynamics by means of an np-dimensional vector. This vector, usually referred to as overparameterized vector, contains all the combinations between the nonlinearity coefficients and the first n samples of the impulse response of the linear block. The estimation of the overparameterized vector is performed with a new regularized kernel-based approach. To this end, we introduce a novel kernel tailored for overparameterized models, which yields estimates that can be uniquely decomposed as the combination of an impulse response and p coefficients of the static nonlinearity. As part of the work, we establish a clear connection between the proposed identification scheme and our recently developed nonparametric method based on the stable spline kernel.
Original languageEnglish
Title of host publication2015 IEEE 54th Annual Conference on Decision and Control (CDC) December 15-18, 2015. Osaka, Japan
Place of PublicationPiscataway
PublisherInstitute of Electrical and Electronics Engineers
Number of pages6
ISBN (Print)9781479978861
Publication statusPublished - 8 Feb 2015
Externally publishedYes
Event54th IEEE Conference on Decision and Control (CDC 2015) - "Osaka International Convention Center", Osaka, Japan
Duration: 15 Dec 201518 Dec 2015
Conference number: 54


Conference54th IEEE Conference on Decision and Control (CDC 2015)
Abbreviated titleCDC 2015
Internet address


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