A non-classical optimal control problem with operator hysteresis nonlinearities

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This article considers a non-classical 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 analogue 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 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 has been 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 optimal control actions for the model case are identified.

作者简介

S. Borzunov

Voronezh State University

Email: mkl150@mail.ru
俄罗斯联邦, Voronezh

P. Meleshenko

Voronezh State University

Email: mkl150@mail.ru
俄罗斯联邦, Voronezh

V. Nesterov

Moscow Aviation Institute (National Research University)

Email: mkl150@mail.ru
俄罗斯联邦, Moscow

M. Semenov

Voronezh State University; Voronezh State Technical University; Federal State Budgetary Educational Institution Federal Research Center “Geophysical Survey of Russia Academy of Sciences

编辑信件的主要联系方式.
Email: mkl150@mail.ru
俄罗斯联邦, Voronezh; Voronezh;

A. Solovyov

JSC Concern Sozvezdie

Email: mkl150@mail.ru
俄罗斯联邦, Voronezh

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