This paper uses the key-term separation principle and develops a multi-innovation stochastic gradient algorithm for Hammerstein MIMO output error systems. The basic idea is to decompose a Hammerstein MIMO system into two subsystems and to identify the parameters of each subsystem interactively. The parameter estimation accuracy can be improved with the innovation length increasing. The simulati...

We numerically investigate the sense in which an adaptive control law achieves internal model control of Hammerstein plants with Prandtl–Ishlinskii hysteresis. We apply retrospective cost adaptive control to a command-following problem for uncertain Hammerstein systems with hysteretic input nonlinearities. The only required modeling information of the linear plant is a single Markov parameter. ...

This paper deals with modeling and parameter identification of nonlinear systems described by Hammerstein model having Piecewise nonlinear characteristics such as Dead-zone nonlinearity characteristic. The simultaneous use of both an easy decomposition technique and the triangular basis functions leads to a particular form of Hammerstein model. The approximation by using Triangular basis functi...

A feedback connection of a Hammerstein system and a linear controller provides a good approach to modeling systems with actuator nonlinearity or input saturation during closed-loop experiments. This paper discusses closed-loop identification of Hammerstein systems where both input and output signals are correlated with noise, and time domain signals are related via a nonlinear map. The static n...

The Two-Stage Algorithm (TSA) has been extensively used and adapted for the identi cation of Hammerstein systems. It is essentially based on a particular formulation of Hammerstein systems in the form of bilinearly parameterized linear regressions. This paper has been motivated by a somewhat contradictory fact: though the optimality of the TSA has been established by Bai in 1998 only in the cas...

In this paper, we show that the residual can be used to estimate the error of a numerical solution for a class of nonlinear Hammerstein equations. It is also shown that the superconvergence of the iterated numerical solution provides a sufficient condition for the residual to be used as an error estimator. Hammerstein equations with smooth as well as wekly singular kernels will be treated.

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...

In this paper, the well known iterated Galerkin method and iterated Galerkin-Kantorovich regularization method for approximating the solution of Fredholm integral equations of the second kind are generalized to Hammerstein equations with smooth and weakly singular kernels. The order of convergence of the Galerkin method and those of superconvergence of the iterated methods are analyzed. Numeric...

In this paper, Hammerstein model and Nonlinear AutoRegressive with eXogeneous inputs (NARX) model are used to represent tubular heat exchanger. Both models have been identified using least squares support vector machines based algorithms. Both algorithms were able to model the heat exchanger system without requiring any apriori assumptions regarding its structure. The results indicate that the ...

In this paper we apply a nonlinear Hammerstein model for speech analysis and coding using frame-based parameter solving. This paper presents a method for calculating the adaptive frame-based coefficients for a Hammerstein model by modifying the residual signal to the desired form. The method is such that the nonlinear and linear coefficients can be obtained without iterations. In experiments th...