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

  • Olga N. SamsonyukEmail author
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 974)

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.

Keywords

Measure-driven differential equations Sweeping process Rate independent hysteresis Impulsive control Space-time representation Optimal control 

Notes

Acknowledgements

The work is partially supported by the Russian Foundation for Basic Research, Project no. 18-01-00026.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Matrosov Institute for System Dynamics and Control Theory SB RASIrkutskRussia

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