Using $\BBH_{2}$-Control Performance Metrics for the Optimal Actuator Location of Distributed Parameter Systems

Abstract

This paper is concerned with the use of H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -control performance metrics in finding optimal actuator locations for a class of infinite-dimensional systems. 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. Minimizing an H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -performance index, parameterized by the possible actuator locations and disturbance functions, leads to optimal locations that in addition to enhanced performance, also provide robustness with respect to the spatial distribution of disturbances. Numerical studies for a cantilever beam and a diffusion problem are used to demonstrate the effects of the spatial distribution of disturbances on the optimal actuator location. The effect of the diffusivity parameter on the best actuator locations is also considered.