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

In this paper, 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...

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Bibliographic Details
Published in:IEEE transactions on automatic control Vol. 68; no. 10; pp. 1 - 8
Main Authors: Khosravi, M., Smith, R. S.
Format: Journal Article
Language:English
Published: New York IEEE 01.10.2023
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Constraints
Convexity
Estimation
Finite impulse response filters
Hilbert space
Identification methods
Impulse response
Kernel
Kernel-based identification method
Kernels
Mathematical analysis
Mathematical models
Numerical stability
Optimization
Regularization
Side-information
Steady state
Steady-state gain
System identification
ISSN:0018-9286, 1558-2523
Online Access:Get full text
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Summary:In this paper, 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.
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ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2023.3243099