Interval Fuzzy Modeling Applied to Wiener Models With Uncertainties

Škrjanc, Igor; Blažič, Sašo; Agamennoni, Osvaldo

doi:10.1109/tsmcb.2005.850166

Cited by 28 publications

(9 citation statements)

References 16 publications

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“…The polynomial degree of B-spline basis functions was set as two (k = 3, piecewise quadratic). The proposed system identification algorithm is carried out with is used for v(t) in order to generate basis functions used in (9). The modelling results are shown in Table I.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…Fundamental to the identification and control of the Wiener system is the characterization/representation of the unknown nonlinear static function. Various approaches have been researched including the nonparametric method [7], subspace model identification methods [8], [6], fuzzy modelling [9] and the parametric method [10], [3], [4], [2]. For the parametric method, the unknown nonlinear function is restricted by some parametric representation with a finite number of parameters, and the system identification includes the estimation of the unknown parameters using nonlinear optimization algorithms based on input/output observational data Based on the approximation theory, the polynomial functions are appropriate in approximating the unknown nonlinear static functions.…”

Section: Introductionmentioning

confidence: 99%

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Wiener system identification using B-spline functions with De Boor recursion

Hong

Mitchell

Chen

2011

Sensor Signal Processing for Defence (SSPD 2011)

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Abstract-A simple and effective algorithm is introduced for the system identification of Wiener system based on the observational input/output data. The B-spline neural network is used to approximate the nonlinear static function in the Wiener system. We incorporate the Gauss-Newton algorithm with De Boor algorithm (both curve and the first order derivatives) for the parameter estimation of the Wiener model, together with the use of a parameter initialization scheme. The efficacy of the proposed approach is demonstrated using an illustrative example.

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Section: Numerical Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Wiener system identification using B-spline functions with De Boor recursion

Hong

Mitchell

Chen

2011

Sensor Signal Processing for Defence (SSPD 2011)

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“…The model characterization/representation of the unknown nonlinear static function in the Wiener model is fundamental to its identification and control. Various approaches have been developed in order to capture the a priori unknown nonlinearity including the nonparametric method (Greblicki 1992), subspace model identification methods Gomez et al 2004), fuzzy modelling (Skrjanc, Blazic, and Agamennoni 2005) and the parametric method (Kalafatis et al 1995(Kalafatis et al , 1997Bai 1998;Zhu 1999). For the parametric method, the unknown nonlinear function is restricted by some parametric representation with a finite number of parameters.…”

Section: Introductionmentioning

confidence: 99%

System identification of Wiener systems with B-spline functions using De Boor recursion

Hong

Mitchell

Chen

2013

International Journal of Systems Science

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In this article a simple and effective algorithm is introduced for the system identification of the Wiener system using observational input/output data. The nonlinear static function in the Wiener system is modelled using a B-spline neural network. The Gauss-Newton algorithm is combined with De Boor algorithm (both curve and the first order derivatives) for the parameter estimation of the Wiener model, together with the use of a parameter initialisation scheme. Numerical examples are utilised to demonstrate the efficacy of the proposed approach. (Billings and Fakhouri 1979;Stoica and So¨derstro¨m 1982;Greblicki and Pawlak 1986;Greblicki 1989Greblicki , 2002Lang 1997;Verhaegen and Westwick 1996;Bai and Fu 2002;Chen 2004;Chaoui, Giri, Rochdi, Haloua, and Naitali 2005;Hong and Mitchell 2007). Alternatively, the Wiener model comprises a linear dynamical model followed by a nonlinear static functional transformation. This is a reasonable model for any linear systems with a nonlinear measurement device, or some industrial/biological systems (Hunter and Korenberg 1986;

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“…Lo and Lin [10] presented robust H ∞ nonlinear modeling and control via uncertain fuzzy systems. Here, the uncertainties are expressed using non-fuzzy uncertain bounding matrices.Skrjanc et al proposed a methodology for interval fuzzy model identification to approximate functions from a finite set of input-output measurements [11][12][13]. This identification method uses the concepts from linear programming and it provides a lower and upper fuzzy model which enclose the whole band of uncertainties.…”

Section: Introductionmentioning

confidence: 99%