Kernel-based Impulse Response Identification with Side-Information on Steady-State Gain

M. Khosravi, R. S. Smith

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In this article, we consider the problem of system identification when side-information is available on the steady-state gain (SSG) of the system. We formulate a general nonparametric identification method as an infinite-dimensional constrained convex program over the reproducing kernel Hilbert space (RKHS) of stable impulse responses. The objective function of this optimization problem is the empirical loss regularized with the norm of RKHS, and the constraint is considered for enforcing the integration of the SSG side-information. The proposed formulation addresses both the discrete-time and continuous-time cases. We show that this program has a unique solution obtained by solving an equivalent finite-dimensional convex optimization. This solution has a closed-form when the empirical loss and regularization functions are quadratic and exact side-information is considered. We perform extensive numerical comparisons to verify the efficiency of the proposed identification methodology.

Original languageEnglish
Pages (from-to)6401-6408
JournalIEEE Transactions on Automatic Control
Issue number10
Publication statusPublished - 2023

Bibliographical note

Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.


  • Estimation
  • Finite impulse response filters
  • Kernel
  • Kernel-based identification method
  • Mathematical models
  • Numerical stability
  • Optimization
  • Side-information
  • Steady-state
  • Steady-state gain


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