ON APPROXIMATELY CONTROLLABLE SYSTEMS SURVEY

Abstract

The aim of this article is to provide a thorough analysis of the approximate controllability of abstract systems, beginning with the inception of the concept in the 1960s. The study begins with a discussion of abstract infinite-dimensional linear systems where the notion of approximate controllability originated. The extension of this foundational theory to nonlinear systems is reviewed, followed by a modern treatment of fractional approximate controllability which has significant applications in the mathematical modeling of phenomena across disciplines.