Kernel-Based Impulse Response Estimation With &lt;italic&gt;a Priori&lt;/italic&gt; Knowledge on the DC Gain

Fujimoto, Yusuke; Sugie, Toshiharu

doi:10.1109/lcsys.2018.2847415

Cited by 18 publications

(15 citation statements)

References 18 publications

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“…D. This method is a general Bayesian variant of the optimal multi-step ahead predictor interpretation of subspace identification approach, where steady-state gain information is integrated into the covariance of the prior distribution [4]. E. In this method, the step response of system is first estimated by a kernel-based Bayesian approach, and then, the FIR is calculated using discrete derivative [50]. F. This method estimates a FIR model for the system based on a kernel-based Bayesian approach where the steadystate gain information is enforced on the total summation of the estimated FIR [51].…”

Section: Numerical Examplesmentioning

confidence: 99%

“…On the other hand, a frequentist framework is employed in [46]- [49], where the steady-state gain side-information is incorporated by imposing linear constraints. Moreover, to leverage the previously mentioned advantages of the kernel-based approach, Bayesian FIR estimation methods are proposed in [50], [51], where kernel-based priors are employed and the steady-state gain side-information is integrated into the resulting estimation problem. The identification scheme in [50] first estimates the step response of the system, and then, the impulse response is obtained via a naïve discrete derivative calculation, which is prone to numerical imprecision and instability.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, to leverage the previously mentioned advantages of the kernel-based approach, Bayesian FIR estimation methods are proposed in [50], [51], where kernel-based priors are employed and the steady-state gain side-information is integrated into the resulting estimation problem. The identification scheme in [50] first estimates the step response of the system, and then, the impulse response is obtained via a naïve discrete derivative calculation, which is prone to numerical imprecision and instability. One the other hand, while the method introduced in [51] improves the estimation performance approach in [50], the proposed formulation is incapable of including deterministic information on the steady-state gain of the system.…”

Section: Introductionmentioning

confidence: 99%

“…The identification scheme in [50] first estimates the step response of the system, and then, the impulse response is obtained via a naïve discrete derivative calculation, which is prone to numerical imprecision and instability. One the other hand, while the method introduced in [51] improves the estimation performance approach in [50], the proposed formulation is incapable of including deterministic information on the steady-state gain of the system. The identification approaches discussed are only applicable when a large set of high-quality data is available.…”

Section: Introductionmentioning

confidence: 99%

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

Khosravi¹,

Smith²

2021

Preprint

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In this paper, we consider the problem of system identification when side-information is available on the steadystate (or DC) gain 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 steady-state gain 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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Section: Numerical Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Khosravi¹,

Smith²

2021

Preprint

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“…In [14,15], the positivity of the system is addressed by imposing structural constraints in the estimation problem. The prior knowledge on the DC-gain of the system is considered in [16]. The kernel-based paradigm is extended to the systems with specific structures, e.g., for Hammerstein and Wiener systems [17,18], networked systems [19], and periodic systems [20].…”

Section: Introductionmentioning

confidence: 99%

On Robustness of Kernel-Based Regularized System Identification

Khosravi¹,

Smith²

2021

Preprint

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This paper presents a novel feature of the kernel-based system identification method. We prove that the regularized kernel-based approach for the estimation of a finite impulse response is equivalent to a robust least-squares problem with a particular uncertainty set defined in terms of the kernel matrix, and thus, it is called kernel-based uncertainty set. We provide a theoretical foundation for the robustness of the kernel-based approach to input disturbances. Based on robust and regularized least-squares methods, different formulations of system identification are considered, where the kernel-based uncertainty set is employed in some of them. We apply these methods to a case where the input measurements are subject to disturbances. Subsequently, we perform extensive numerical experiments and compare the results to examine the impact of utilizing kernel-based uncertainty sets in the identification procedure. The numerical experiments confirm that the robust least square identification approach with the kernel-based uncertainty set improves the robustness of the estimation to the input disturbances.

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On embeddings and inverse embeddings of input design for regularized system identification

Chen²,

Kong³

et al. 2023

Automatica

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Kernel-Based Impulse Response Estimation With <italic>a Priori</italic> Knowledge on the DC Gain

Cited by 18 publications

References 18 publications

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

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

On Robustness of Kernel-Based Regularized System Identification

On embeddings and inverse embeddings of input design for regularized system identification

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