Approximate Controllability of Second-Order Evolution Differential Inclusions in Hilbert Spaces

In this paper, we consider a class of second-order evolution differential inclusions in Hilbert spaces. This paper deals with the approximate controllability for a class of second-order control systems. First, we establish a set of sufficient conditions for the approximate controllability for a clas...

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Bibliographic Details
Published in:Mediterranean journal of mathematics 2016-10, Vol.13 (5), p.3433-3454
Main Authors: Mahmudov, N. I., Vijayakumar, V., Murugesu, R.
Format: Article
Language:English
Subjects:
Control systems
Controllability
Evolution
Fixed points (mathematics)
Hilbert space
Inclusions
Mathematics
Mathematics and Statistics
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Summary:In this paper, we consider a class of second-order evolution differential inclusions in Hilbert spaces. This paper deals with the approximate controllability for a class of second-order control systems. First, we establish a set of sufficient conditions for the approximate controllability for a class of second-order evolution differential inclusions in Hilbert spaces. We use Bohnenblust–Karlin’s fixed point theorem to prove our main results. Further, we extend the result to study the approximate controllability concept with nonlocal conditions and also extend the result to study the approximate controllability for impulsive control systems with nonlocal conditions. An example is also given to illustrate our main results.
ISSN:1660-5446
1660-5454
DOI:10.1007/s00009-016-0695-7