Approximate controllability of infinite dimensional bilinear systems

摘要

The aim of this paper is to study approximate controllability for bilinear systems in the general case. The existence and uniqueness of solutions to bilinear evolution equations are ob- tained. The paper shows that the approximate controllability of the bilinear control problem is equivalent to the approximate controllability of a discrete problem, using the method developed by Loreti and Siconolfi to approximate the bilinear control problem in an infinite-dimensional Banach space by means of a sequence of discrete problems. Finally, the necessary conditions for The bilinear system to be approximately controllable are state and proved.