Existence and Uniqueness of Optimal Control for a Distributed-Parameter Bilinear System

In this paper, we study an optimal control problem of bilinear type. The system is governed by a fourth-order parabolic operator. The performance index is of the form J(u) = ∫0TL(z(t), u(t)) dt. Under suitable hypotheses, it is shown that there exists an optimal control ū and it satisfies an appropriate optimality system. Further, for a small initial state ū is unique.