  Optimal actuator design for a vibration control problem is calculated. The
actuator shape is optimized according to the closed-loop performance of the
resulting linear-quadratic regulator and a penalty on the actuator size. The
optimal actuator shape is found by means of shape calculus and a topological
derivative of the linear-quadratic regulator (LQR) performance index. An
abstract framework is proposed based on the theory for infinite-dimensional
optimization of both the actuator shape and the associated control problem. A
numerical realization of the optimality condition is presented for the actuator
shape using a level-set method for topological derivatives. A Numerical example
illustrating the design of actuator for Euler-Bernoulli beam model is provided.
