This paper presents an original approach for nonlinear Volterra and NARMAX filter identification. We propose here to use a non persistent excitation of input sequence to excite few terms of the Volterra and NARMAX filter, which must satisfy a set of physical constraints. Expressions have been developped to evaluate the accurate number of excited terms of the Volterra and NARMAX filter.

In this paper we present a new approach for linear Volterra integral equations that is based on optimal control theory. Some optimal control problems corresponding Volterra integral equation be introduced which we solve these problems by discretization methods and linear programming approaches. Finally, some examples are given to show the efficiency of approach. Index Terms —Volterra integral e...

The Volterra series can be used to model a large subset of nonlinear, dynamic systems. A major drawback is the number of coefficients required model such systems. In order to reduce the number of required coefficients, Laguerre polynomials are used to estimate the Volterra kernels. Existing literature proposes algorithms for a fixed number of Volterra kernels, and Laguerre series. This paper pr...

This paper mainly studied the LMS adaptive filter algorithm to the Volterra system model. Through the construction of the second order Volterra system model, the application of respectively selecting the first order and second order variable step length de-correlation Volterra LMS algorithm in gaussian noise environment, when the input signals in different correlation coefficient, the iteration...

In this article, by means of considering an isospectral operator equation which corresponds to the Volterra lattice, and constructing opportune time evolution problems with negative powers of spectral parameter, and using discrete zero curvature representation, negative Volterra flows are proposed. We also propose the mixed Volterra flows, which come from positive and negative volterra flows. F...

Discrete-time Volterra models play an important role in many application areas. The main drawback of these models is their parametric complexity due to the huge number of their parameters, the kernel coefficients. Using the symmetry property of the Volterra kernels, these ones can be viewed as symmetric tensors. In this paper, we apply tensor decompositions (PARAFAC and HOSVD) for reducing the ...

In the present paper we introduce a notion of homotopy of two Volterra operators which is related to fixed points of such operators. It is establish a criterion when two Volterra operators are homotopic, as a consequence we obtain that the corresponding tournaments of that operators are the same. This, due to [4], gives us a possibility to know some information about the trajectory of homotopic...

Nonlinear adaptive filtering techniques are widely used for the nonlinearities identification in manny applications. This paper investigates the performances of the Volterra estimator by considering a nonlinear system identification application. The Volterra estimator parameters are compared with those of a linear estimator. For the nonlinear estimator, based on a second order RLS Volterra filt...

A great many of processes in a nature are nonlinear, so their modeling requires an embedding of nonlinear parts into the model structure. One of the popular approaches to the nonlinear system modeling are Volterra series. Unfortunately, already the second order Volterra kernel requires high amount of coefficients for its identification and therefore a large number of computations for its realiz...

Abstract In this article, first, we present an example of fuzzy normed space by means the Mittag-Leffler function. Next, extend concept to matrix valued and also introduce a class control functions stabilize nonlinear ϕ -Hadamard fractional Volterra integro-differential equation. sense, investigate Ulam–Hyers–Rassias stability for kind equations in Banach space. Finally, as application, using f...