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. ...

In this paper, we analyse the iterated collocation method for Hammerstein equations with smooth and weakly singular kernels. The paper expands the study which began in [14] concerning the superconvergence of the iterated Galerkin method for Hammerstein equations. We obtain in this paper a similar superconvergence result for the iterated collocation method for Hammerstein equations. We also disc...

In this paper, a novel algorithm is developed for identifying Hammerstein model. The static nonlinear function is characterized by function link artificial neural network (FLANN) and the linear dynamic subsystem by an ARMA model. The utilization of FLANN can not only result in a simple and effective representation of static nonlinearity but also simplify the learning algorithm. A two-step proce...

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

System identification (SI) is the discipline of inferring mathematical models from unknown dynamic systems using input/output observations such with or without prior knowledge some system parameters. Many valid algorithms are available in literature, including Volterra series expansion, Hammerstein–Wiener models, nonlinear auto-regressive moving average model exogenous inputs (NARMAX) and its d...

A nonlinear Hammerstein model is proposed for coding speech signals. Using Tsay’s nonlinearity test, we first show that the great majority of speech frames contain nonlinearities (over 80% in our test data) when using 20-millisecond speech frames. Frame length correlates with the level of nonlinearity: the longer the frames the higher the percentage of nonlinear frames. Motivated by this result...

reliability wiener number is a modification of the original wiener number in which probabilities are assigned to edges yielding a natural model in which there are some (or all) bonds in the molecule that are not static. various probabilities naturally allow modelling different types of chemical bonds because chemical bonds are of different types and it is well-known that under certain condition...

In this paper a new system identification algorithm is introduced for Hammerstein systems based on observational input/output data. The nonlinear static function in the Hammerstein system is modelled using a non-uniform rational B-spline (NURB) neural network. The proposed system identification algorithm for this NURB network based Hammerstein system consists of two successive stages. First the...

Abstract This paper investigates the accuracy of the linear component that forms part of an overall Hammerstein model-structure estimate, and a key finding is that the process of estimating the non-linear element can have a strong effect on the associated estimate of the linear dynamics. Furthermore, this effect is not explained simply by way of considering how the input spectrum is changed by ...

Partial plant knowledge may be used to develop model-based extremum seekers; however, existing results rely on a type of time-scale separationwhich leads to slow optimization relative to the plant dynamics. In this work, a fast model-based extremum seeking scheme is proposed for a Hammerstein plant, and semi-global stability results are provided. The structure of a Hammerstein plant is used to ...