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Please use this identifier to cite or link to this item: http://hdl.handle.net/11129/4127

Title: Partial Approximate Controllability of Semilinear Control Systems
Authors: Bashirov, Agamirza
Ghahramanlou, Noushin Houshyar
Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics
Keywords: Mathematics
Applied Mathematics and Computer Science
Controllability
approximate controllability
exact controllability
partial controllability
semilinear systems
stochastic systems
Issue Date: Sep-2015
Publisher: Eastern Mediterranean University EMU
Citation: Ghahramanlou, Noushin Houshyar. (2015). Partial Approximate Controllability of Semilinear Control Systems. Thesis (Ph.D.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.
Abstract: Most of the controllability concepts are for first ordered differential equations, while not all the control systems are of this kind; but by increasing the dimension of the state space, one can rewrite the control system in the form of first ordered differential equations. Therefore, it seems useful to define partial controllability concepts which maintain the original state space. In this thesis, a sufficient condition for partial approximate controllability of semilinear deterministic control systems is proved with a technique which is completely different from the methods using fixed point theorems. More specifically, the partial S-controllability has been weakened for partially observable semilinear stochastic systems and a sufficient condition is provided. The results obtained are demonstrated within examples. Keywords: Controllability, approximate controllability, exact controllability, partial controllability, semilinear systems, stochastic systems.
ÖZ: Kontrol edilebilirlik kavramlarının ço˘gu, birinci dereceden diferansiyel denklemlerı içeren kontrol sistemleri için formüle edilmi¸stir. Do˘gadaki bütün diferansiyel denklem sistemleri bu tür de˘gildir, ama alanın boyutunu geni¸sleterek bu formda yazılmı¸s olabilir. Bu nedenle, orijinal alanı korumak kısmi kontrol edilebilirlik kavramları tanımlamak yararlı görünüyor. Bu tezde, yarı-lineer deterministik kontrol sistemlerinin kısmi yakla¸sık kontrol edilebilirlik için yeterli bir ko¸sul, sabit nokta teoremleri yöntemlerinden tamamen farklı bir teknik ile kanıtlanmı¸stır. Dahası, kısmen gözlemlenebilir yarı-lineer stokastik sistemleri için zayıflatılmı¸s kısmi S-kontrol edilebilirlik incelenmi¸s ve bu kontrol edilebilirlik kavramı için yeterli bir ko¸sul sa˘glanmı¸stır. Elde edilen sonuçlar, örneklerle gösterilmi¸stir. Anahtar Kelimeler: Kontrol edilebilirlik, yakla¸sık kontrol edilebilirlik, tam kontrol edilebilirlik, kısmi kontrol edilebilirlik, yarı-lineer sistemler, stokastik sistemler.
Description: Doctor of Philosophy in Applied Mathematics and Computer Science. Thesis (Ph.D.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2015. Supervisor: Prof. Dr. Agamirza Bashirov.
URI: http://hdl.handle.net/11129/4127
Appears in Collections:Theses (Master's and Ph.D) – Mathematics

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