In this paper, we propose a novel algorithm for the identification of Hammerstein systems. Adopting a Bayesian approach, we model the impulse response of the unknown linear dynamic system as a realization of a zero-mean Gaussian process. The covariance matrix (or kernel) of this process is given by the recently introduced stable-spline kernel, which encodes information on the stability and regu...

Of the many model structures that can represent a nonlinear process effectively, the Hammerstein model is one such model which has attracted a lot of attention. This paper considers a real industrial problem of modelling a nonlinear multivariable steam generating plant using the methods of system identification. The work uses Hammerstein model to model the plant from sampled data collected at A...

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...

The Two-Stage Algorithm (TSA) has been extensively used and adapted for the identi cation of Hammerstein systems. It essentially deals with the parameter estimation problem for a linear regression parameterized in a bilinear form. This paper is motivated by a somewhat contradictory fact: though the optimality of the TSA has been established only in the case of some special weighting matrices, t...

Convergence criterion of the inexact methods is established for operators with hölder continuous first derivatives. An application to a special nonlinear Hammerstein integral equation of the second kind is provided.

We investigate local convergence of an SQP method for non-linear optimal control of weakly singular Hammerstein integral equations. Suucient conditions for local quadratic convergence of the method based are discussed.

Degenerate kernel approximation method is generalized to solve Hammerstein system of Fredholm integral equations of the second kind. This method approximates the system of integral equations by constructing degenerate kernel approximations and then the problem is reduced to the solution of a system of algebraic equations. Convergence analysis is investigated and on some test problems, the propo...

A new nonparametric approach to identify multivariable Hammerstein models is presented in this paper. The linear dynamic subsystem is identified and represented by its finite impulse response (FIR) model, and, the static nonlinearity is identified and represented as an MIMO input-output mapping. By specially designed test signals, the estimation of FIRs for multivariable linear subsystems can b...