The optimal control of an elastically connected rectangular plate–membrane system by point-wise actuators is considered. Problems of the type are of significant practical interest in most real mechanical structures widely used in aeronautical, civil, naval, and mechanical engineering. An index of performance is formulated, which consists of a modified energy functional of the two coupled structure at a specified time and penalty functions involving the point control actuators. Necessary conditions of optimality are derived in the form of independent integral equations which lead to explicit expressions for the point-wise actuators. The results are applied to a specific problem, and numerical results are given that reveal the effectiveness of the proposed control mechanism.
