Banach fixed-point theorem in semilinear controllability problems – a survey

Klamka, J.; Babiarz, A.; Niezabitowski, M.

doi:10.1515/bpasts-2016-0004

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Tytuł artykułu

Banach fixed-point theorem in semilinear controllability problems – a survey

Autorzy

Klamka J. , Babiarz A. , Niezabitowski M.

Treść / Zawartość

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DOI

10.1515/bpasts-2016-0004

Warianty tytułu

Języki publikacji

Abstrakty

The main aim of this article is to review the existing state of art concerning the complete controllability of semilinear dynamical systems. The study focus on obtaining the sufficient conditions for the complete controllability for various systems using the Banach fixedpoint theorem. We describe the results for stochastic semilinear functional integro-differential system, stochastic partial differential equations with finite delays, semilinear functional equations, a stochastic semilinear system, a impulsive stochastic integro-differential system, semilinear stochastic impulsive systems, an impulsive neutral functional evolution integro-differential system and a nonlinear stochastic neutral impulsive system. Finally, two examples are presented.

Słowa kluczowe

complete controllability Banach space Hilbert space fixed-point infinite dimensional space

sterowność przestrzeń Banacha przestrzeń Hilberta

Wydawca

Polska Akademia Nauk, Wydział IV Nauk Technicznych

Czasopismo

Bulletin of the Polish Academy of Sciences. Technical Sciences

Rocznik

2016

Tom

Vol. 64, nr 1

Strony

21--35

Opis fizyczny

Bibliogr. 80 poz.

Twórcy

autor

Klamka J.

Institute of Automatic Control, Silesian University of Technology, 16 Akademicka St., 44-100 Gliwice, Poland

autor

Babiarz A.

Artur.Babiarz@polsl.pl

Institute of Automatic Control, Silesian University of Technology, 16 Akademicka St., 44-100 Gliwice, Poland

autor

Niezabitowski M.

Institute of Automatic Control, Silesian University of Technology, 16 Akademicka St., 44-100 Gliwice, Poland

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Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016.

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