scholarly journals A new convergence analysis for the Volterra series representation of nonlinear systems

Automatica ◽  
2020 ◽  
Vol 111 ◽  
pp. 108599 ◽  
Author(s):  
Yun-Peng Zhu ◽  
Z.Q. Lang
Keyword(s):  
Nonlinear Systems ◽  
Convergence Analysis ◽  
Volterra Series ◽  
Series Representation

scholarly journals Identification of Nonlinear Systems: Volterra Series Simplification

10.14311/976 ◽  
2007 ◽  
Vol 47 (4-5) ◽  
Author(s):  
A. Novák
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Transfer Function ◽  
Linear System ◽  
Impulse Response ◽  
Volterra Series ◽  
Series Representation ◽  
Multimedia Systems ◽  
Audio Amplifier ◽  
Enormous Number

Traditional measurement of multimedia systems, e.g. linear impulse response and transfer function, are sufficient but not faultless. For these methods the pure linear system is considered and nonlinearities, which are usually included in real systems, are disregarded. One of the ways to describe and analyze a nonlinear system is by using Volterra Series representation. However, this representation uses an enormous number of coefficients. In this work a simplification of this method is proposed and an experiment with an audio amplifier is shown. 

Instantaneous Identification of Polynomial Nonlinearity Based on Volterra Series Representation

2005 ◽  
Vol 293-294 ◽  
pp. 703-710 ◽  
Author(s):  
Giacomo V. Demarie ◽  
Rosario Ceravolo ◽  
Alessandro de Stefano
Keyword(s):  
Structural Engineering ◽  
Volterra Series ◽  
Series Representation ◽  
Consistent Estimate ◽  
Short Time Fourier Transform ◽  
Dynamic Identification ◽  
Polynomial Nonlinearity ◽  
Definition Of ◽  
Short Time

In structural engineering applications a sufficient quantity of experimental data to be able to achieve a consistent estimate of nonlinear quantities is seldom available: this applies in particular when the structures are to be tested in situ. This report discusses the definition of instantaneous estimators to be used in the dynamic identification of invariant nonlinear systems on the basis of Short-Time Fourier Transform representation of excitation and system’s response and within the framework of a Volterra series representation of the input/output relationship. An estimation of the parameters of a dynamic system can be worked out from the evolution of such instantaneous estimators.

scholarly journals Memory in a New Variant of King’s Family for Solving Nonlinear Systems

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1251
Author(s):  
Munish Kansal ◽  
Alicia Cordero ◽  
Sonia Bhalla ◽  
Juan R. Torregrosa
Keyword(s):  
Nonlinear Systems ◽  
Convergence Analysis ◽  
Numerical Experiments ◽  
Order Of Convergence ◽  
Recent Literature ◽  
Divided Difference ◽  
Difference Operators ◽  
New Variant ◽  
Order Four ◽  
With Memory

In the recent literature, very few high-order Jacobian-free methods with memory for solving nonlinear systems appear. In this paper, we introduce a new variant of King’s family with order four to solve nonlinear systems along with its convergence analysis. The proposed family requires two divided difference operators and to compute only one inverse of a matrix per iteration. Furthermore, we have extended the proposed scheme up to the sixth-order of convergence with two additional functional evaluations. In addition, these schemes are further extended to methods with memory. We illustrate their applicability by performing numerical experiments on a wide variety of practical problems, even big-sized. It is observed that these methods produce approximations of greater accuracy and are more efficient in practice, compared with the existing methods.

On Convergence of Volterra Series Expansion of a Class of Nonlinear Systems

2017 ◽  
Vol 19 (3) ◽  
pp. 1089-1102 ◽  
Author(s):  
Xingjian Jing ◽  
Zhenlong Xiao
Keyword(s):  
Nonlinear Systems ◽  
Series Expansion ◽  
Volterra Series
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