Abstract
In this study, we consider a regional controllability problem for a class of distributed bilinear systems evolving in a spatial domain Omega. A feedback control is used to steer the system state close to a desired profile at a final time T, only on omega a subregion of the system domain which may be interior or on the boundary of Omega. Our purpose is to prove that an optimal control exists, and characterised as a solution to an optimality system. Numerical algorithm is given and successfully illustrated by simulations.