Approximate controllability of second-order evolution differential inclusions in Hilbert spaces

TL;DR

This paper investigates the approximate controllability of second-order evolution differential inclusions in Hilbert spaces, establishing sufficient conditions and extending results to nonlocal and impulsive control systems using fixed point theorems.

Contribution

It introduces new sufficient conditions for approximate controllability of second-order differential inclusions, including nonlocal and impulsive cases, using Bohnenblust-Karlin's fixed point theorem.

Findings

Established sufficient conditions for approximate controllability.

Extended results to nonlocal and impulsive control systems.

Provided an illustrative example.

Abstract

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 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.