A relaxation result for unbounded control system with hysteresis

Sergey A. Timoshin

doi:10.1016/j.jmaa.2015.11.008

A relaxation result for unbounded control system with hysteresis

Sergey A. Timoshin^*

^*Corresponding author for this work

RAS - Matrosov Institute for System Dynamics and Control Theory, Siberian Branch

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

We consider a control system of two ODEs describing a hysteresis effect. The term unbounded in the title refers to the fact that the multivalued mapping giving the control constraints may admit unbounded values. Being at the same time nonconvex valued, we convexify the constraint and we approximate solutions of thus obtained relaxed problem by those of the given system. The property of Lipschitz continuity of the multivalued mapping traditionally employed for such kind of relaxation problems is weakened to a more appropriate in the context of unbounded valued multifunctions "truncated" version of it.

Original language	English
Pages (from-to)	1036-1053
Number of pages	18
Journal	Journal of Mathematical Analysis and Applications
Volume	435
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2015.11.008
Publication status	Published - 2016
Externally published	Yes

Keywords

Evolution system
Hysteresis
Relaxation
Relaxed lipschitz condition
Unbounded controls

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10.1016/j.jmaa.2015.11.008

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AB - We consider a control system of two ODEs describing a hysteresis effect. The term unbounded in the title refers to the fact that the multivalued mapping giving the control constraints may admit unbounded values. Being at the same time nonconvex valued, we convexify the constraint and we approximate solutions of thus obtained relaxed problem by those of the given system. The property of Lipschitz continuity of the multivalued mapping traditionally employed for such kind of relaxation problems is weakened to a more appropriate in the context of unbounded valued multifunctions "truncated" version of it.

KW - Evolution system

KW - Hysteresis

KW - Relaxation

KW - Relaxed lipschitz condition

KW - Unbounded controls

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A relaxation result for unbounded control system with hysteresis

Abstract

Keywords

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