System identification in the presence of trends and outliers using sparse optimization

Shirdel, Amir H.; Böling, Jari M.; Toivonen, Hannu

doi:10.1016/j.jprocont.2016.05.008

Cited by 11 publications

(5 citation statements)

References 26 publications

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“…This relates our CT definition singular order

q

with the notion of structured sparsity (or group sparse signal 22 ) associated with the DT perturbation terms. In DT, the problem of parameters and switching times estimation is generally performed in batch mode using, for example, sparse optimization techniques, 23 while this note mainly focuses on the real time estimation of the vector parameter in a CT setting.…”

Section: Impulsive Modelsmentioning

confidence: 99%

Online continuous time system identification in the presence of impulsive terms

Belkoura

2022

Adaptive Control & Signal

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Online parameters estimation algorithms are proposed for continuous time systems subject to structured perturbations. Using a distribution framework, a matrix pencil structure, whose polynomial order is characterized by the nature of the singularities describing the impulsive effects, is proposed for the modeling of perturbed systems with different disturbance types. Then, using an appropriate projection subspace, the rectangular pencils are reformulated as square generalized eigenvalue problems subject to linear constraints, from which unperturbed regression are derived. This approach allows for the implementation of recursive estimation schemes, free of penalty terms. An identifiability analysis is also conducted, and theoretical results are illustrated with experimental and simulated data.

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“…This relates our CT definition singular order

q

Section: Impulsive Modelsmentioning

confidence: 99%

Online continuous time system identification in the presence of impulsive terms

Belkoura

2022

Adaptive Control & Signal

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“…It is important to detect and account for gross errors properly, as they may deteriorate the identification accuracy. If the measurements were completely collected in a batch manner, gross errors could be detected and removed by data preprocessing or the problem of system identification could be tackled by nonsmooth optimization-based estimators (Bako, 2016; Bako and Ohlsson, 2016; Shirdel et al, 2016; Xu et al, 2014). However, these available batch identification methods do not apply any more for recursive identification of TV systems.…”

Section: Introductionmentioning

confidence: 99%

Novel adaptive methods for output-only recursive identification of time-varying systems subject to gross errors

Ding

Zhou

2019

Journal of Vibration and Control

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Gross errors are generally used to model intermittent sensor failures and occasional data packet losses or corruption, which arise in many engineering communities. In this work, we propose to deal with the problem of output-only recursive identification of time-varying systems subject to gross errors by using an adaptive weighting and forgetting combined strategy. Under the assumption that gross errors are unknown and can be of arbitrarily large magnitude, time-dependent autoregressive model-based adaptive recursive identification methods are proposed by minimizing the sum of norm errors and achieving a sparse prediction error sequence. The adaptive weighting strategy is used to deemphasize data observations contaminated by gross errors, and the forgetting mechanism is used to deemphasize data from the remote past, allowing the proposed methods to track time-varying dynamics of the system subject to gross errors. The proposed methods are numerically and experimentally tested, and the comparative results demonstrate the superior time-varying tracking capability of the proposed methods in extremely challenging gross error circumstances.

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“…In the literature, a large number of models have been utilized for representing outliers, some of which are non‐Gaussian distributions such as α ‐stable noise, t‐distribution, and amplitude‐modulated binary‐state sequence such as Bernoulli‐Gaussian . Furthermore, for the purpose of outlier detection, outlying measurements has been represented deterministically . It is almost universal in the literature of the Hammerstein modeling that the estimation algorithms are based on either minimizing the sum of squares of prediction errors, ie, least squares (LS), or quadratic Lyapunov function.…”

Section: Introductionmentioning

confidence: 99%

“…34,35 Furthermore, for the purpose of outlier detection, outlying measurements has been represented deterministically. 36,37 It is almost universal in the literature of the Hammerstein modeling that the estimation algorithms are based on either minimizing the sum of squares of prediction errors, ie, least squares (LS), or quadratic Lyapunov function. These identification methods are proved efficient under the assumption that the measurement noises are Gaussian.…”

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confidence: 99%

Robust identification of MISO neuro‐fractional‐order Hammerstein systems

Rahmani

Farrokhi

2019

Intl J Robust & Nonlinear

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Summary This paper introduces a multiple‐input–single‐output (MISO) neuro‐fractional‐order Hammerstein (NFH) model with a Lyapunov‐based identification method, which is robust in the presence of outliers. The proposed model is composed of a multiple‐input–multiple‐output radial basis function neural network in series with a MISO linear fractional‐order system. The state‐space matrices of the NFH are identified in the time domain via the Lyapunov stability theory using input‐output data acquired from the system. In this regard, the need for the system state variables is eliminated by introducing the auxiliary input‐output filtered signals into the identification laws. Moreover, since practical measurement data may contain outliers, which degrade performance of the identification methods (eg, least‐square–based methods), a Gaussian Lyapunov function is proposed, which is rather insensitive to outliers compared with commonly used quadratic Lyapunov function. In addition, stability and convergence analysis of the presented method is provided. Comparative example verifies superior performance of the proposed method as compared with the algorithm based on the quadratic Lyapunov function and a recently developed input‐output regression‐based robust identification algorithm.

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System identification in the presence of trends and outliers using sparse optimization

Cited by 11 publications

References 26 publications

Online continuous time system identification in the presence of impulsive terms

Online continuous time system identification in the presence of impulsive terms

Novel adaptive methods for output-only recursive identification of time-varying systems subject to gross errors

Robust identification of MISO neuro‐fractional‐order Hammerstein systems

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