Reproducing kernel functions based univariate spline interpolation

Geng, Fazhan; Wu, Xinyuan

doi:10.1016/j.aml.2021.107525

Cited by 29 publications

(10 citation statements)

References 15 publications

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“…The proposed algorithm also has a deal with multivariate system identification by replacing lags inputs in NARX to variables of multivariate system. The proposed methods in this article can combined other estimation algorithms [50][51][52][53][54] to study the parameter identification issues of linear and nonlinear systems [55][56][57][58][59] and can be applied to other fields [60][61][62][63][64][65][66] such as information processing and engineering application systems [67][68][69][70][71][72][73][74][75][76][77][78] and process control systems.…”

Section: Discussionmentioning

confidence: 99%

Modeling nonlinear systems using the tensor network B‐spline and the multi‐innovation identification theory

Wang

Tang

Deng

2022

Intl J Robust & Nonlinear

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The nonlinear autoregressive exogenous (NARX) model shows a strong expression capacity for nonlinear systems since these systems have limited information about their structures. However, it is difficult to model the NARX system with a relatively high dimension by using the popular polynomial NARX and the neural network efficiently. This article uses the tensor network B-spline (TNBS) to model the NARX system, whose representation of the multivariate B-spline weight tensor can alleviate the computation and store burden for processing high-dimensional systems. Furthermore, applying the multi-innovation identification theory and the hierarchical identification principle, the recursive algorithm by combining the l 2 -norm is proposed to the NARX system with Gaussian noise. Because of the local adjustability of the B-spline curve, the TNBS can fit nonlinear systems with strong nonlinearity by the meaning of setting a proper degree and knots number. Finally, a numerical experiment is given to demonstrate the effectiveness of the proposed algorithm.

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Section: Discussionmentioning

confidence: 99%

Modeling nonlinear systems using the tensor network B‐spline and the multi‐innovation identification theory

Wang

Tang

Deng

2022

Intl J Robust & Nonlinear

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“…The proof can be referred to the work in References 19 and 71 and that is omitted here. The proposed approaches in the article can combine other mathematical tools [72][73][74][75] and statistical strategies [76][77][78][79][80][81] to investigate the identification methods of nonlinear systems with different structures and disturbance noises and can be applied to literatures [82][83][84][85][86][87][88][89][90][91] such as engineering application systems.…”

Section: The Convergence Analysis For the O-rls And O-sg Algorithmsmentioning

confidence: 99%

Overall recursive least squares and overall stochastic gradient algorithms and their convergence for feedback nonlinear controlled autoregressive systems

Wei

Xiao

et al. 2022

Intl J Robust & Nonlinear

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This article deals with the problems of the parameter estimation for feedback nonlinear controlled autoregressive systems (i.e., feedback nonlinear equation‐error systems). The bilinear‐in‐parameter identification model is formulated to describe the feedback nonlinear system. An overall recursive least squares algorithm is developed to handle the difficulty of the bilinear‐in‐parameter. For the purpose of avoiding the heavy computational burden, an overall stochastic gradient algorithm is deduced and the forgetting factor is introduced to improve the convergence rate. Furthermore, the convergence analysis of the proposed algorithms are established by means of the stochastic process theory. The effectiveness of the proposed algorithms are illustrated by the simulation example.

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“…The methods proposed in this article can combine some statistical tools and optimal strategies [84][85][86][87][88][89][90] to study the parameter estimation algorithms of linear and nonlinear systems [91][92][93][94][95][96][97] and can be applied to other fields [98][99][100][101][102][103][104] such as engineering systems. Then, the AM-MI-RGLS algorithm in ( 20)-( 28) for the input nonlinear OEAR system with piecewise-linear nonlinearity consists of the following steps.…”

Section: The Am-mi-rgls Algorithmmentioning

confidence: 99%

Filtering‐based multi‐innovation recursive identification methods for input nonlinear systems with piecewise‐linear nonlinearity based on the optimization criterion

Fan

Liu

2022

Optim Control Appl Methods

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Piecewise-linear nonlinearity is an effective representation for hard nonlinearities such as saturation, dead zone, and backlash, which can be also used as a general tool for approximating nonlinear characteristics. For the input piecewise-linear output-error autoregressive systems, we develop a parametric expression of the piecewise-linear nonlinearity through a switching function and position functions, and derive the identification model of the system by using the key item separation. Based on the optimization criterion, an auxiliary model-based multi-innovation recursive generalized least-squares algorithm is deduced for estimating the unknown parameters according to the obtained model. Since the system is disturbed by colored noise, we introduce the data filtering technique from a view point of improving the parameter estimation accuracy. The filtering identification model of the system is derived and a filtering-based multi-innovation recursive generalized least-squares algorithm is proposed. The simulation example demonstrates the effectiveness of the proposed algorithms and shows that the filtering-based multi-innovation recursive generalized least-squares algorithm has better identification performance.

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Reproducing kernel functions based univariate spline interpolation

Cited by 29 publications

References 15 publications

Modeling nonlinear systems using the tensor network B‐spline and the multi‐innovation identification theory

Modeling nonlinear systems using the tensor network B‐spline and the multi‐innovation identification theory

Overall recursive least squares and overall stochastic gradient algorithms and their convergence for feedback nonlinear controlled autoregressive systems

Filtering‐based multi‐innovation recursive identification methods for input nonlinear systems with piecewise‐linear nonlinearity based on the optimization criterion

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