Optimal control of a bilinear distributed system with incomplete data

The aim of this paper is to study an optimal control problem for a bilinear abstract system with missing data. Our idea consists to construct an iterative sequence to transform the original problem into a sequence of linear problem. Under some hypothesis, we prove the convergence of linearised problem to the bilinear problem. These may also to obtain the optimality system for the original problem. The effectiveness of our approach will be illustrated by a simple application.