Convergence of direct recursive algorithm for identification of Preisach hysteresis model with stochastic input

TL;DR

This paper proves exponential convergence of a recursive algorithm for identifying Preisach hysteresis model parameters using stochastic input data, providing explicit convergence rate estimates and analyzing influencing factors.

Contribution

It introduces a convergence proof and rate estimation for a recursive identification algorithm based on stochastic inputs, extending classical deterministic methods.

Findings

Proves exponential convergence of the recursive algorithm.

Provides explicit estimates for the convergence rate.

Analyzes how input properties affect convergence speed.

Abstract

We consider a recursive iterative algorithm for identification of parameters of the Preisach model, one of the most commonly used models of hysteretic input-output relationships. The classical identification algorithm due to Mayergoyz defines explicitly a series of test inputs that allow one to find parameters of the Preisach model with any desired precision provided that (a) such input time series can be implemented and applied; and, (b) the corresponding output data can be accurately measured and recorded. Recursive iterative identification schemes suitable for a number of engineering applications have been recently proposed as an alternative to the classical algorithm. These recursive schemes do not use any input design but rather rely on an input-output data stream resulting from random fluctuations of the input variable. Furthermore, only recent values of the input-output data streams are available for the scheme at any time instant. In this work, we prove exponential convergence of such algorithms, estimate explicitly the convergence rate, and explore which properties of the stochastic input and the algorithm affect the guaranteed convergence rate.