Title: Optimal Actuator Location for H∞ Control (½ hour)
Abstract: In engineering applications, actuators are frequently used as mechanisms to introduce or to prevent motion. The effectiveness of an actuator is improved by placing it at an optimal location. For example, in aerospace engineering, the flight wings are mounted with square shaped piezoelectric patches that are placed at an optimal location to suppress the vibration. The central focus of the research has been on finding the optimal actuator location. The objective of H∞ control is to design a controller that minimizes the effect of disturbance on output. In this work, the objective function is the optimal disturbance attenuation at the given actuator location. Although the state-space for the original problem is infinite-dimensional, control engineers have published several results on optimal actuator location only for an approximated problem. In this work, we first show continuity of the optimal disturbance attenuation as a function of actuator location. Next, the conditions necessary for convergence of the optimal cost and the corresponding actuator location for the infinite-dimensional problem are established. Lastly, we will briefly describe the numerical calculation of optimal actuator location for H∞ control.