Convergence of Direct Recursive Algorithm for Identification of Preisach Hysteresis Model with Stochastic Input

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. This online algorithm uses a simple rule for updating the values of the piecewise constant density function in the switching region at each time step. The so-called persistent excitation condition has been shown to play an important role for convergence of recursive iteration schemes when input-output data are generated by a deterministic input (such as, for example, a periodically repeated sequence of test inputs prescribed by the classical Mayergoyz identification algorithm). In this work, we assume that the input randomly fluctuates and these fluctuations can be described by a stochastic Markov process. Assuming that accurate measurements of the input and output are available, we prove the exponential convergence of the recursive identification algorithm, estimate explicitly the convergence rate, and explore which properties of the stochastic input and the algorithm affect the guaranteed convergence rate. An analogue of the persistent excitation condition suitable for analysis of stochastic Markov inputs is established. Numerical examples that test the convergence of the algorithm in the case of a time-dependent density function and in the presence of measurement noise are presented.