Optimal scanning control of flexible structures in two-dimensional space

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.