<abstract xmlns="http://www.w3.org/1999/xhtml"><p> The main objective of this article is to present the state of the art concerning approximate controllability of dynamic systems in infinite-dimensional spaces. The presented investigation focuses on obtaining sufficient conditions for approximate controllability of various types of dynamic systems using Schauder’s fixed-point theorem. We describe the results of approximate controllability for nonlinear impulsive neutral fuzzy stochastic differential equations with nonlocal conditions, impulsive neutral functional evolution integro-differential systems, stochastic impulsive systems with control-dependent coefficients, nonlinear impulsive differential systems, and evolution systems with nonlocal conditions and semilinear evolution equation.</p></abstract>

The main objective of this article is to present the state of the art concerning approximate controllability of dynamic systems in infinite-dimensional spaces. The presented investigation focuses on obtaining sufficient conditions for approximate controllability of various types of dynamic systems using Schauder’s fixed-point theorem. We describe the results of approximate controllability for nonlinear impulsive neutral fuzzy stochastic differential equations with nonlocal conditions, impulsive neutral functional evolution integro-differential systems, stochastic impulsive systems with control-dependent coefficients, nonlinear impulsive differential systems, and evolution systems with nonlocal conditions and semilinear evolution equation.

Schauder’s fixed-point theorem in approximate controllability problems

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

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Schauder\u2019s fixed-point theorem in approximate controllability problems"}

The main objective of this article is to present the state of the art concerning approximate controllability of dynamic systems in infinite-dimensional spaces....

Schauder’s fixed-point theorem in approximate controllability problems

Published Online: Jul 02, 2016

Page range: 263 - 275

Received: Sep 14, 2015

Accepted: Jan 29, 2016

DOI: https://doi.org/10.1515/amcs-2016-0018

Keywords
approximate controllability, Banach space, Hilbert space, Schauder’s fixed-point theorem, infinite-dimensional space.

© by Artur Babiarz

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Schauder’s fixed-point theorem in approximate controllability problems

Published Online: Jul 02, 2016

Page range: 263 - 275

Received: Sep 14, 2015

Accepted: Jan 29, 2016

DOI: https://doi.org/10.1515/amcs-2016-0018

Keywordsapproximate controllability, Banach space, Hilbert space, Schauder’s fixed-point theorem, infinite-dimensional space.

© by Artur Babiarz

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
approximate controllability, Banach space, Hilbert space, Schauder’s fixed-point theorem, infinite-dimensional space.