In this work, a weighted least squares (WLS) based adaptive tracker is designed for a class of Hammerstein systems. Incorporating with the diminishing excitation technique, the proposed adaptive tracker leads to the minimality of the tracking errors and strong consistency of the estimates for the unknown system parameters. A numerical example is given and the simulation results are consistent w...

The convergence theorems for the stochastic approximation (SA) algorithm with expanding truncations are first presented, which the system identification methods discussed in the paper are essentially based on. Then, the recursive identification algorithms are respectively defined for the multivariate errors-in-variables systems, Hammerstein systems, and Wiener systems. All estimates given in th...

Compactly supported linear semiorthogonal B-spline wavelets together with their dual wavelets are developed to approximate the solutions of nonlinear Fredholm-Hammerstein integral equations. Properties of these wavelets are first presented; these properties are then utilized to reduce the computation of integral equations to some algebraic equations. The method is computationally attractive, an...

We study the numerical solvability of a class of nonlinear weakly singular integral equations of Volterra-Hammerstein type with noncompact kernels. We obtain existence and uniqueness results and analyze the product integration methods for these equations under some verifiable conditions on the kernels and nonlinear functions. The convergence analysis is investigated and finally numerical experi...

We present regularization methods for solving ill-posed Hammerstein type operator equations under weaker conditions than in earlier studies such as [13]. Our semilocal convergence analysis is based on majorizing sequences. Numerical examples where the new convergence criteria are satisfied but the old criteria are not satified are also presented at the end of the study. AMS (MOS) Subject Classi...

Based on the fixed point index theory for a Banach space, nontrivial periodic solutions are found for a class of integral equation of the form φ(x) = Z [x,x+ω]∩Ω K(x, y)f(y, φ(y − τ(y))) dy, x ∈ Ω, where Ω is a closed subset of RN with perioidc structure. Nonlinear Hammerstein integral equations of the form