The existence and uniqueness of solutions for kernel-based system identification

Khosravi, Mohammad; Smith, Roy S.

doi:10.1016/j.automatica.2022.110728

Cited by 10 publications

(2 citation statements)

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“…[1][2][3][4][5] In recent years, nonlinear system identification and parameter estimation problems have attracted an increasing amount of research interest. [6][7][8][9] Various models are employed to describe the actual nonlinear system, such as the Volterra model [10][11][12][13][14] and the nonlinear time series (NTS) model, [15][16][17] which are efficient for predicting future values and for controlling random vibrations by utilizing current and past data. 18 Compared with the Volterra model which involves the convolution of the input-output and has a complex structure, the NTS model is formulated as a linear ensemble of several nonlinear functions, thus it can be considered a natural extension of the typical linear models.…”

Section: Introductionmentioning

confidence: 99%

“…System identification is an essential tool for enhancing control performance and for achieving robust fault‐tolerant behavior 1–5 . In recent years, nonlinear system identification and parameter estimation problems have attracted an increasing amount of research interest 6–9 . Various models are employed to describe the actual nonlinear system, such as the Volterra model 10–14 and the nonlinear time series (NTS) model, 15–17 which are efficient for predicting future values and for controlling random vibrations by utilizing current and past data 18 .…”

Section: Introductionmentioning

confidence: 99%

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Cauchy kernel correntropy‐based robust multi‐innovation identification method for the nonlinear exponential autoregressive model in non‐Gaussian environment

Zhao,

Wang,

Liu

2024

Intl J Robust & Nonlinear

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This paper discusses the identification problem of the nonlinear exponential autoregressive model in the non‐Gaussian noise environment. To suppress the negative influence caused by the non‐Gaussian noise on the accuracy of the identification, this paper employs a Cauchy kernel correntropy‐based criterion function to present a robust gradient algorithm for calculating the parameter estimates of the model. To solve the difficulty of selecting the step‐size in the gradient algorithm, this paper derives an optimal step‐size related to the bandwidth of the Cauchy kernel. Moreover, in order to improve the accuracy of the parameter estimations, a Cauchy kernel correntropy‐based robust multi‐innovation identification method is developed by utilizing the multi‐innovation identification theory. Two simulation examples exhibit that the proposed algorithms can effectively reduce the negative influence of the non‐Gaussian noise on parameter estimation in contrast with the conventional least mean squares algorithm.

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