Stochastic Model of a Hysteresis Converter with a Domain Structure

This study is devoted to generalizing one of the most popular constructive models of hysteresis, the Preisach converter (a continuous system of nonideal relays connected in parallel). In many applied problems related to modeling hysteresis effects, where the domain structure of carriers of the hysteresis properties is a priori assumed (multiple magnetization reversal of ferromagnetic components of electromagnetic systems, polarization of a ferroelectric depending on the electric field strength, dependence of employment on price in monocommodity markets, etc.), the uncertainties in the reactions of individual domains to external actions need to be taken into account. In this paper, we propose an instrumental method that makes it possible to take into account such uncertainties by stochastic models of the elementary carriers of hysteresis properties. The main properties of discrete and continuous relay systems are considered, whose parameters are treated as random variables, while the output of the relay system is represented as a random process. The correctness of the definition is investigated; in particular, the independence of the output (of a random process) from the sampling method within the limit transition from a finite to a continuous system of nonideal relays is established, and the controllability and monotonicity (in the corresponding definition) of the stochastic analog of the Preisach converter are established.