Combined $\mathcal{H}_{\infty}$ linear parameter varying control design and optimal sensor/actuator selection

This paper presents an approach to combine H∞ dynamic output feedback controller design for linear parameter-varying (LPV) systems with optimal selection of sensors and actuators. This concurrent design problem is formulated as a Mixed Boolean Semi-Definite Programming (MBSDP) optimization problem. By means of the Big-M reformulation, the boolean decision variables related to the selection of sensors and actuators are decoupled from the SDP problem underlying the H∞ controller synthesis. This reformulation allows us to solve the initial NP-hard problem using a Branch and Bound (BNB) algorithm. The concurrent design of an LPV vibration controller and optimal actuator selection for a smart composite plate serves as a case study to validate the developed approach.