Using ℍ2-control metrics for the optimal actuator location of infinite-dimensional systems

This paper considers control performance metrics to find the optimal actuator locations for a class of infinite-dimensional systems. By examining the H₂ optimal value, parameterized by the candidate actuator locations, one arrives at optimal locations that in addition to enhanced performance, also provide a robustness with respect to the spatial distribution of disturbances. Conditions that guarantee convergence of the optimal actuator location for the finite-dimensional representation of the infinite-dimensional system to the optimal actuator location of the original infinite-dimensional system are provided. Essentially they require that the input operator corresponding to the candidate actuator locations satisfies a compactness condition. Numerical studies for a cantilever beam are used to demonstrate the effects of the spatial distribution of disturbances on the optimal actuator location.