Concurrent design of an active vibration feedback controller and actuator/sensor selection for a composite plate

This article presents two approaches to simultaneously select optimal locations of sensors and actuators and design of a $\mathcal{H}_{\infty}$ dynamic output feedback controller. The first approach discussed in this paper is based on an iterative reweighted $\ell_{1}$ norm regularization, an heuristic approach. The second approach converts the combined design into mixed boolean semi-definite programming optimization problem (MBSDP). A branch and bound (BNB) algorithm is adopted to solve this convex optimization problem to give a global optimal solution in terms of selection and control design. The two approaches are compared with an exhaustive search in terms of optimality and is applied to a vibration rejection control design of a composite plate.