Strong Consistency Of Parameter Estimates Research Articles

The Hammerstein–Wiener Model for Identification of Stochastic Systems

Identification of nonlinear stochastic systems in the class of Hammerstein–Wiener models is studied. The problem is specific due to the nonlinearities of the investigated object. Hammerstein–Wiener models are constructed with regard for the disturbances of the type of white noise and martingale sequence at the output of the object. A two-stage recursive identification algorithm is designed. Necessary and sufficient conditions for the strong consistency of parameter estimates found by this algorithm are formulated. The results are applied to adaptive tracking of the output of an object.

Strong consistency of parameter estimates in direct self-tuning control algorithms based on stochastic approximation

In this paper convergence of the regulator parameter estimates generated by direct self-tuning control algorithms of stochastic approximation type is considered. The process is supposed to be represented by an ARMAX model with an arbitrary delay, while a dither signal converging to zero in the mean-square sense is superimposed on a deterministic reference. The strong consistency of the regulator parameter estimates is proved under assumptions concerning the estimator complexity and the properties of the optimal regulator transfer function for a broad class of dither signals. The impact of a priori information on the dimension of the estimator and the consistency of the parameter estimates is indicated. It is demonstrated that the classical persistence of excitation condition is not satisfied for the analyzed algorithms.