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2019 | OriginalPaper | Chapter

The Space-Time Representation for Optimal Impulsive Control Problems with Hysteresis

Author : Olga N. Samsonyuk

Published in: Optimization and Applications

Publisher: Springer International Publishing

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Abstract

An optimal control problem for a sweeping process driven by impulsive controls is considered. The control system we study is described by both a measure-driven differential equation and a differential inclusion. This system is the impulsive-trajectory relaxation of an ordinary control system with nonlinearity of hysteresis type, in which the hysteresis is modeled by the play operator and considered as a particular case of a nonconvex sweeping process. The concept of a sweeping process for the so-called graph completions of functions of bounded variation, defining the corresponding moving set, is developed. The space-time representation based on the singular space-time transformation and a method to obtain optimality conditions for impulsive processes are proposed. By way of motivation, an example from mathematical economics is considered.

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Title: The Space-Time Representation for Optimal Impulsive Control Problems with Hysteresis
Author: Olga N. Samsonyuk
Publisher: Springer International Publishing
Book: Optimization and Applications
Print ISBN: 978-3-030-10933-2

Electronic ISBN: 978-3-030-10934-9

Copyright Year: 2019
DOI: https://doi.org/10.1007/978-3-030-10934-9_25

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