A relaxation result for unbounded control system with hysteresis

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:435

Article

Timoshin, Sergey A.¹ 

[1] Russian Acad Sci, Inst Syst Dynam & Control Theory, Siberian Branch, Lermontov Str 134, Irkutsk 664033, Russia

关键词: Evolution system;    Unbounded controls;    Hysteresis;    Relaxation;    Relaxed Lipschitz condition;   

DOI  :  10.1016/j.jmaa.2015.11.008

来源: Elsevier

【 摘 要 】

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. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free