Let H be a real Hilbert space. Let K, F : H → H be bounded, continuous and monotone mappings. Suppose that u∗ ∈ H is a solution to Hammerstein equation u + KFu = 0. We introduce a new explicit iterative sequence and prove strong convergence of the sequence to a solution of the Hammerstein equation.

The aim of the given paper is the development of an approach for parametric identification of Hammerstein systems with piecewise linear nonlinearities, i.e., when the saturation-like function with unknown slopes is followed by a linear part with unknown parameters. It is shown here that by a simple input data rearrangement and by a following data partition the problem of identification of a non...

In this work we develop two different adaptive control schemes for a class of nonlinear systems. The class of systems belongs to the Hammerstein-Wiener nonlinear systems. The techniques developed are presented and an example is given in illustration. Using an approximate inverse of the nonlinear plant model, the overall system is forced to track the desired reference signal.

Positive solutions of systems of Hammerstein integral equations are studied by using the theory of the fixed-point index for compact maps defined on cones in Banach spaces. Criteria for the fixed-point index of the Hammerstein integral operators being 1 or 0 are given. These criteria are generalizations of previous results on a single Hammerstein integral operator. Some of criteria are new and ...

In the previous work our research group introduced an exact solution to the Hammerstein system and is known as H-BEST (Hammerstein BlockOriented Exact Solution Technique). It was later expanded to multiple input, multiple output (MIMO) Hammerstein and Wiener (W-BEST) systems. This work is extends this approach to more complicated block-oriented systems, namely a Hammerstein-Wiener process. By e...

A new method for capacity and spectral efficiency increases is a full-duplex communication, where sending receiving are done simultaneously. Hence, severe interference leaked from the transmitter to receiver, which can disrupt system’s operation completely. For reduction, transceiver tries estimate interfering symbols remove their effects. typical use Hammerstein model. In this method, nonlinea...

A new PID tuning and controller approach is introduced for Hammerstein systems based on input/output data. A B-spline neural network is used to model the nonlinear static function in the Hammerstein system. The control signal is composed of a PID controller together with a correction term. In order to update the control signal, the multistep ahead predictions of the Hammerstein system based on ...

In this paper the existence of a positive measurable solution of the Hammerstein equation of the first kind with a singular nonlinear term at the origin is presented. 0. Introduction The literature on the Hammerstein equations with the reciprocal of the solution in the integrand is rather limited, although there are many applications. For example, the equation

While there exists a substantial literature on the identification of Hammerstein and Wiener models, the identification of WienerHammerstein models has received considerably less attention yet this is a model class of very great practical importance. This paper proposes an elegant approach to estimating Wiener-Hammerstein systems from measured data.

A numerical method for solving nonlinear mixed Hammerstein integral equations is presented in this paper. The method is based upon hybrid of rationalized Haar functions approximations. The properties of hybrid functions which are the combinations of block-pulse functions and rationalized Haar functions are first presented. The Newton-Cotes nodes and Newton-Cotes integration method are then util...