Identification of discrete Hammerstein systems using kernel regression estimates

Greblicki, Wlodzimierz

doi:10.1109/tac.1986.1104096

Cited by 161 publications

(68 citation statements)

References 15 publications

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“…Under the fully nonparametric assumptions 1-4, not the genuine characteristic m (x) but a nonlinearity μ (x) = λ 0 m (x) + ζ (where ζ = Em (x 1 ) · i>0 λ i is a system dependent constant) can at most be identified On-line wavelet estimation of Hammerstein system nonlinearity 515 from input-output data (Greblicki and Pawlak, 1986). Indeed, since the following holds:…”

Section: Remarkmentioning

confidence: 99%

“…. (note that μ (x) = m (x) with this setting, see the work of Greblicki and Pawlak (1986)). The noise had the uniform distribution with the amplitude set such that NSR {m/z}…”

Section: Experimental Illustrationmentioning

confidence: 99%

“…convergence conditions and convergence rates, are shown to be the same as those of off-line algorithms, cf. the results of Greblicki and Pawlak (1986) or Hsu et al (2008). The Hammerstein system ( Fig.…”

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confidence: 99%

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On-line wavelet estimation of Hammerstein system nonlinearity

Śliwiński¹

2010

International Journal of Applied Mathematics and Computer Science

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A new algorithm for nonparametric wavelet estimation of Hammerstein system nonlinearity is proposed. The algorithm works in the on-line regime (viz., past measurements are not available) and offers a convenient uniform routine for nonlinearity estimation at an arbitrary point and at any moment of the identification process. The pointwise convergence of the estimate to locally bounded nonlinearities and the rate of this convergence are both established.

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Section: Remarkmentioning

confidence: 99%

“…. (note that μ (x) = m (x) with this setting, see the work of Greblicki and Pawlak (1986)). The noise had the uniform distribution with the amplitude set such that NSR {m/z}…”

Section: Experimental Illustrationmentioning

confidence: 99%

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On-line wavelet estimation of Hammerstein system nonlinearity

Śliwiński¹

2010

International Journal of Applied Mathematics and Computer Science

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“…A wide range of identification methods have also been developed for this type of model structure, see e.g. Bai (1998); Greblicki and Pawlak (1986); Goethals et al (2005); Zhu (2000); Crama and Schoukens (2001); Ding and Chen (2005); Cai and Bai (2011);Vanbeylen et al (2008); Wang et al (2009) ;Liu and Bai (2007).…”

Section: Introductionmentioning

confidence: 99%

Finite model order accuracy in Hammerstein model estimation

Hjalmarsson

Mårtensson

2012

Automatica

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Hammerstein models is one of the most commonly used model classes used for identifying nonlinear systems. A static input nonlinearity followed by a linear dynamical part is an adequate way to model many real-life systems. This paper investigates the asymptotic (in terms of sample size) variance of Hammerstein model estimates. The work extends earlier results by Ninness and Gibson (2002) in the following ways. Not only frequency function estimation but estimation of general quantities is considered. The expressions are not restricted to be valid asymptotically in the model order. In addition, the results cover model structures having noise models and allow for data generated under feedback. The increase in variance due to the estimation of the input nonlinearity is characterized. In particular, under open loop operation, white additive noise and the assumption of a separable process, it is shown that the variance increase is exactly a term that was observed in Ninness and Gibson (2002) to result in good agreement with simulations. This term vanishes in the formal asymptotic in model order analysis in Ninness and Gibson (2002).

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“…The Hammerstein model, comprising a nonlinear static functional transformation followed by a linear dynamical model, has been widely researched [3,21,2,12]. The model characterization/representation of the unknown nonlinear static function is fundamental to the identification of Hammerstein model.…”

Section: Introductionmentioning

confidence: 99%

PSO Assisted NURB Neural Network Identification

Hong

Chen

2012

Lecture Notes in Computer Science

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Abstract.A system identification algorithm is introduced for Hammerstein systems that are modelled using a non-uniform rational B-spline (NURB) neural network. The proposed algorithm consists of two successive stages. First the shaping parameters in NURB network are estimated using a particle swarm optimization (PSO) procedure. Then the remaining parameters are estimated by the method of the singular value decomposition (SVD). Numerical examples including a linear pole assignment controller are utilized to demonstrate the efficacy of the proposed approach.

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Identification of discrete Hammerstein systems using kernel regression estimates

Cited by 161 publications

References 15 publications

On-line wavelet estimation of Hammerstein system nonlinearity

On-line wavelet estimation of Hammerstein system nonlinearity

Finite model order accuracy in Hammerstein model estimation

PSO Assisted NURB Neural Network Identification

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