This article presents a survey of various methods for nonparametric identification of nonlinear systems. Nonparametric identification methods are those that measure Wiener kernels or Volterra kernels, since an output of a nonlinear system can be described by the convolution integral of Wiener or Volterra kernels and the system input. Section 1 highlights the representation methods of nonlinear ...

in this paper, an effective numerical method is introduced for the treatment of nonlinear two-dimensional volterra-fredholm integro-differential equations. here, we use the so-called two-dimensional block-pulse functions.first, the two-dimensional block-pulse operational matrix of integration and differentiation has been presented. then, by using this matrices, the nonlinear two-dimensional vol...

This paper presents a new and efficient transient analysis method for mildly nonlinear circuits. The method is based on Volterra series representation of nonlinear circuits. It characterizes nonlinear circuits using a set of linear circuits called Volterra circuits. The input of the first-order Volterra circuit is identical to that of the nonlinear circuit, whereas that of higher order Volterra...

This paper proposes a new reduced complexity Volterra model called S-PARAFAC-Volterra. The proposed model is yielded by using the symmetry property of the Volterra kernels and their tensor decomposition using the PARAFAC technique. It takes advantage from previous results where an algorithm for the estimation of the memory and the order of the Volterra model has been presented. The proposed mod...

In this paper, an effective numerical method is introduced for the treatment of nonlinear two-dimensional Volterra-Fredholm integro-differential equations. Here, we use the so-called two-dimensional block-pulse functions.First, the two-dimensional block-pulse operational matrix of integration and differentiation has been presented. Then, by using this matrices, the nonlinear two-dimensional Vol...

This is a short tutorial on Volterra and Wiener series applications to modelling of nonlinear systems and phenomena, and also a survey of the recent achievements in this area. In particular, we show here how the philosophies standing behind each of the above theories differ from each other. On the other hand, we discuss also mathematical relationships between Volterra and Wiener ker...

in this paper, we present a numerical method for solving nonlinear fredholm and volterra integral equations of the second kind which is based on the use of haar wavelets and collocation method. we use properties of block pulse functions (bpf) for solving volterra integral equation. numerical examples show efficiency of the method.

in this letter, the numerical scheme of nonlinear volterra-fredholm integro-differential equations is proposed in a reproducing kernel hilbert space (rkhs). the method is constructed based on the reproducing kernel properties in which the initial condition of the problem is satis ed. the nonlinear terms are replaced by its taylor series. in this technique, the nonlinear volterra-fredholm integr...

In this paper, we establish some new retarded nonlinear Volterra-Fredholm type integral inequalities with maxima in two independent variables, and we present the applications to research the boundedness of solutions to retarded nonlinear Volterra-Fredholm type integral equations.

In this paper, an effective numerical method is introduced for the treatment of nonlinear two-dimensional Volterra-Fredholm integro-differential equations. Here, we use the so-called two-dimensional block-pulse functions.First, the two-dimensional block-pulse operational matrix of integration and differentiation has been presented. Then, by using this matrices, the nonlinear two-dimensional Vol...