This paper analyzes the computational complexity of set membership identification of Hammerstein and Wiener systems. Its main results show that, even in cases where a portion of the plant is known, the problems are generically NP-hard both in the number of experimental data points and in the number of inputs (Wiener) or outputs (Hammerstein) of the nonlinearity. These results provide new insigh...

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 ...

In this paper we consider the solutions to two neighbouring Hammerstein-type Volterra integral equations of the form

Here a posteriori error estimate for the numerical solution of nonlinear Voltena- Hammerstein equations is given. We present an error upper bound for nonlinear Voltena-Hammastein integral equations, in which the form of nonlinearity is algebraic and develop a posteriori error estimate for the recently proposed method of Brunner for these problems (the implicitly linear collocation method)...

Due to the lack of powerful model description methods, the identification of Hammerstein systems based on the non-uniform input-output dataset remains a challenging problem. This paper introduces a time-varying backward shift operator to describe periodically non-uniformly sampled-data Hammerstein systems, which can simplify the structure of the lifted models using the traditional lifting techn...

The purpose of this paper is two-fold. First, we develop the Petrov-Galerkin method and the iterated Petrov-Galerkin method for a class of nonlinear Hammerstein equations. Alpert [1] established a class of wavelet basis and applied it to approximate solutions of the Fredholm second kind integral equations by the Galerkin method. He then demonstrated an advantage of a wavelet basis application t...

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...

When using Bai’s method for estimating the coefficients of both the linear and nonlinear parts of a Hammerstein model, there is no guarantee that the resulting linear filter will be stable. To obtain a stable linear filter the well-known minimum phase correction can be used. However, if it used without some compensation in the nonlinear part, one obtains a Hammerstein model with no theoretical ...

The prevailing analyses of sinusoidally perturbed extremum-seeking (ES) schemes require the ES scheme to act slowly relative to the plant dynamics. Existing analyses that do allow for fast ES are fairly restrictive, considering only local behaviour on Wiener–Hammerstein plants where the nonlinear element is quadratic. In this paper, semi-global stability of an ES scheme acting on a general Hamm...