A response approximation method for stochastically excited, nonlinear, dynamic systems is presented. Herein, the output of the nonlinear system is approximated by a finite-order Volterra series. The original nonlinear system is replaced by a bilinear system in order to determine the kernels of this Volterra series. The parameters of the bilinear system are determined by minimizing the differenc...

This paper deals with the identification and the control of nonlinear processes described by input -output models, such as parametric Volterra models. In particular, we extend an adaptive predictive algorithm without taking into account constraints. The calculation of the control law can be posed as a thirdorder nonlinear program. The building algorithm is based on a new approach using a convol...

This paper deals with the identification and the control of nonlinear processes described by input -output models, such as parametric Volterra models. In particular, we extend an adaptive predictive algorithm without taking into account constraints. The calculation of the control law can be posed as a thirdorder nonlinear program. The building algorithm is based on a new approach using a convol...

A new solution for the problem of selecting poles of the two-parameter Kautz functions in Volterra models is proposed. In general, a large number of parameters are required to represent the Volterra kernels, although this difficulty can be overcome by describing each kernel using a basis of orthonormal functions, such as the Kautz basis. This representation has a Wiener structure consisting of ...

We present a new mixed finite element method for class of parabolic equations with p-Laplacian and nonlinear memory. The applicability, stability convergence the are studied. First, problem is written in formulation as system one equation Volterra equation. Then, discretized space variable using Lagrangian basis degree r?1. Finally, Cranck-Nicolson trapezoidal quadrature applied to discretize t...

The objective of this paper is t o present a new structure f o r an adaptive nonlinear equalizer f o r digital transmission over a nonlinear satellite channel with PSK modulation. The adaptive nonlinear equalizer is based o n a discrete frequencydomain third-order Volterra filter with the multidimensional overlap-save filtering technique, and o n the block least mean square (BLMS) algorithm f o...

The semidiscretization in space of Volterra-Fredholm integral equations (arising, for example, as mathematical models of the spreading of epidemics) leads to large systems of Volterra integral equations. Here, we study inexpensive timestepping methods using certain DQ (= direct quadrature) methods which are employed in a way that exploits the local superconvergence properties of spatial colloca...

This article introduces two Tensor Train-based iterative algorithms for the identification of high order discrete-time nonlinear MIMO Volterra systems. The system identification problem is rewritten in terms of a Volterra tensor, which is never explicitly constructed, thus avoiding the curse of dimensionality. It is shown how each iteration of the two identification algorithms involves solving ...

Abstract: A new exact method of measuring the Volterra kernels of finite order discrete nonlinear systems is presented. The kernels are rearranged in terms of multivariate crossproducts in the vector form. The one-, two-, . . . , and `-dimensional kernel vectors are determined using a deterministic multilevel sequence with ` distinct levels at the input of the system. It is shown that the defin...