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Analysis and control of differential inclusions with anti-periodic conditions

Published online by Cambridge University Press:  16 May 2014

Z. H. Liu  and
S. Migórski
Z. H. Liu
Affiliation:
Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis and College of Sciences, Guangxi University for Nationalities, Nanning, Guangxi 530006, People's Republic of China, (zhhliu@hotmail.com)
S. Migórski
Affiliation:
Jagiellonian University, Faculty of Mathematics and Computer Science, Institute of Computer Science, ul. ᴌojasiewicza 6, 30348 Krakow, Poland, (stanislaw.migorski@ii.uj.edu.pl)
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Abstract

We deal with the optimal control of systems driven by differential inclusions with anti-periodic conditions in Banach spaces. The operators in the differential inclusions, describing the control system, all depend on control variables. By a solution of the control system we mean a ‘trajectory-control’ pair. We first prove that, for fixed control variables, the set of solutions is non-empty for the corresponding differential inclusion with anti-periodic conditions. We then show the functional-topological properties of the set of solutions. Finally, we investigate the existence of solutions to the optimal control problem. These abstract results can be used to study optimal control systems of evolutionary hemi-variational inequalities.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 144 , Issue 3 , June 2014 , pp. 591 - 602
Copyright
Copyright © Royal Society of Edinburgh 2014 

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