Stochastic model of the hysteresis converter with a domain structure

The work is devoted to generalization of one of the most "popular" constructive models of hysteresis – the Preisach converter (a continuous system of non-ideal relays connected in parallel). In many applied problems related to modeling hysteresis effects, where the domain structure of carriers of 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 mono-commodity markets, etc.), one has to face with the need to take into account the uncertainties in the reactions of individual domains to external influences. In this paper, we propose an instrumental method that makes it possible to take into account such uncertainties by means of stochastic models of elementary carriers of hysteresis properties. The basic properties of discrete and continuous relay systems are considered, the parameters of which 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 discrete to a continual system of nonideal relays is established, and the controllability and monotonicity (within the framework of the corresponding definition) of the stochastic analogue of the Preisach converter are established.