Nonclassical Optimal Control Problem with Operator Hysteresis Nonlinearities

This article considers a nonclassical optimal control problem, in which the dynamics of an object is described by a system of differential operator equations with a hysteresis converter on the right side. The hysteresis dependence is formalized using an analog of the Preisach converter with inverted threshold numbers, which reflects the nonlinear and multivalued dependence of consumer demand on the price of goods. This allows us to take into account the history of consumer relations over a finite time interval. The problem of optimal production, storage, and sales of products on a mono-commodity market under conditions of a hysteresis demand function is set and solved. The conditions of solvability of the problem under the conditions of applicability of the maximum principle of L.S. Pontryagin are given. The conditions under which the solution is unique are given. The article also presents the results of computational experiments in which the optimal control actions for the model case are identified.