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Abstract: A class of optimal control problems for hyperbolic systems in two-dimensional space is considered. An approach is proposed to damp the undesirable vibrations in the structures by pointwise moving force actuators extending over the spatial region occupied by the structure. A class of performance indices is introduced that includes functions of the state variable, its first and second-order space derivatives and first-order time derivative evaluated at a preassigned terminal time, and a suitable penalty term involving the control forces. A maximum principle is given for such general scanning control problem that facilitates the determination of the unique optimal control. A solution method is developed for the active vibration control of plates of general shape. The implementation of the method is presented and the effectiveness of a single moving force actuator is investigated and compared to a single fixed force actuator by a specific numerical example. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]