A semi-parametric algorithm for identification of Hammerstein systems in the presence of correlated noise is proposed. The procedure is based on the non-parametric kernel regression estimator and the standard least squares. The advantages of the method in comparison with the standard non-parametric approach are discussed. Limit properties of the proposed estimator are studied, and the simulatio...

An ordinary differential equation with a parameter in the boundary conditions describes the steady state in an adiabatic tubular chemical reactor. In this paper, the problem is considered as a Hammerstein integral equation and solutions are obtained using Adomian’s decomposition method.

In this paper we analyse the iterated discrete Legendre Galerkin method for Fredholm-Hammerstein integral equation with a smooth kernel. Using a sufficiently accurate numerical quadrature rule, we obtain super-convergence rates for the iterated discrete Legendre Galerkin solutions in both infinity and L-norm. Numerical examples are given to illustrate the theoretical results.

The aim of this paper is to present an existence theorem for the operator equation of Hammerstein type x + KF (x) = 0 with the discontinuous semimonotone operator F . Then the result is used to prove the existence of solution of the equations of Urysohn type. Some examples in the theory of nonlinear equations in Lp(Ω) are given for illustration.

Integral equations of mixed Voltera-Fredholm type arise in various physical and biological problems. In the present paper, we obtain the approximate solution of the nonlinear Volterra-Hammerstein integral equations of mixed type in terms of Taylor polynomial. The reliability and efficiency of the proposed scheme are demonstrated by some numerical experiments.

The paper deals with parameter identification of nonlinear dynamic systems using Hammerstein-Wiener models. Multiple application of a decomposition technique provides special expressions for the model description that are linear in parameters. This allows iterative estimation of all model parameters based on the measured input/output data and estimates of internal variables. The proposed algori...

In the note the class of block-oriented dynamic nonlinear systems is considered, in particular, Hammerstein and Wiener systems are investigated. Several algorithms for nonlinear system identification are presented. The algorithms exploit various degrees of prior knowledge from parametric to nonparametric. Eventually, a semiparametric algorithm, which shares advantages of both approaches is anno...

A new method for identifying Hammerstein/Wiener models is proposed, where the parameters of a piecewise linear characteristic and a linear transfer function are estimated by recursive least-squares (RLS). Using smooth validity functions and an adaptive algorithm for optimal partitioning of the local linear models an efficient and accurate model can be identified.

It is presented in this paper a method for designing a nonlinear model predictive controller. The controller is based on a hybrid Wiener-Hammerstein fuzzy-neural predictive model and а simplified gradient optimization algorithm. The proposed approach is used to control the product temperature in a Lyophlization plant. The controller efficiency is tested and proved by simulation experiments in M...