In this paper, we establish some results for a Volterra–Hammerstein integral equation with modified arguments: existence and uniqueness, inequalities, monotony Ulam-Hyers-Rassias stability. We emphasize that many problems from the domain of symmetry are modeled by differential equations those approached in stability point view. literature, Fredholm, Volterra Hammerstein integrals symmetric kern...

In this paper, interval Legendre wavelet method is investigated to approximated the solution of the interval Volterra-Fredholm-Hammerstein integral equation. The shifted interval Legendre polynomials are introduced and based on interval Legendre wavelet method is defined. The existence and uniqueness theorem for the interval Volterra-Fredholm-Hammerstein integral equations is proved. Some examp...

In this article, we study the exact controllability of an abstract model described by the controlled generalized Hammerstein type integral equation

This paper deals with modelling and parameter identification of nonlinear systems described by Hammerstein model having asymmetric static nonlinearities known as preload nonlinearity characteristic. The simultaneous use of both an easy decomposition technique and the generalized orthonormal bases leads to a particular form of Hammerstein model containing a minimal parameters number. The employ ...

using the mean-value theorem for integrals we tried to solved the nonlinear integral equations of hammerstein type . the mean approach is to obtain an initial guess with unknown coefficients for unknown function y(x). the procedure of this method is so fast and don't need high cpu and complicated programming. the advantages of this method are that we can applied for those integral equation...

The maximum correntropy criterion (MCC) has recently been successfully applied to adaptive filtering. Adaptive algorithms under MCC show strong robustness against large outliers. In this work, we apply the MCC criterion to develop a robust Hammerstein adaptive filter. Compared with the traditional Hammerstein adaptive filters, which are usually derived based on the well-known mean square error ...

Self-tuning control with recursive identification of extremal dynamic systems is considered. The systems can be represented by combinations of linear dynamic and extremal static parts, their output being disturbed by a coloured noise. Minimumvariance controllers for Hammerstein, Wiener, and Wiener-Hammerstein-type systems are designed taking into consideration restrictions for control signal ma...

A new method for the control reconfiguration of stable Hammerstein systems after actuator faults is described. The class of Hammerstein systems contains input-saturated systems, which are ubiquitous in practice. The new reconfiguration approach uses a virtual actuator that permits to keep the nominal controller in the loop. The concept of virtual actuators is extended to reflect the nonlinear p...

A recursive algorithm is proposed in this paper to identify Hammerstein–Wiener systems with heteroscedastic measurement noise. Based on the parameterization model of Hammerstein–Wiener systems, the algorithm is derived by minimizing the expectation of the sum of squared parameter estimation errors. By replacing the immeasurable internal variables with their estimations, the need for the commonl...

The problem of the identification of Hammerstein and Wiener models is considered in this paper. The suggested approach in this paper utilizes the spectral magnitude matching method that minimizes the sum squared error between the spectral magnitudes evaluated for a number of short-time frames of the measured output signal of the nonlinear system and the output signal of the nonlinear model. The...