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Optimal actuator design for a vibration control problem is calculated. Theactuator shape is optimized according to the closed-loop performance of theresulting linear-quadratic regulator and a penalty on the actuator size. Theoptimal actuator shape is found by means of shape calculus and a topologicalderivative of the linear-quadratic regulator (LQR) performance index. Anabstract framework is proposed based on the theory for infinite-dimensionaloptimization of both the actuator shape and the associated control problem. Anumerical realization of the optimality condition is presented for the actuatorshape using a level-set method for topological derivatives. A Numerical exampleillustrating the design of actuator for Euler-Bernoulli beam model is provided.

Optimal actuator design for vibration control based on LQR performance and shape calculus