Convergence of ℋ∞-optimal actuator locations

In control of vibrations, diffusion and many other problems governed by partial differential equations, there is freedom in the choice of actuator location. The actuator location should be chosen to optimize performance objectives. In this paper, we consider ℋ∞ performance with state-feedback. It is shown that the corresponding optimal actuator problem is well-posed. In practice, approximations are used to determine the optimal actuator location. The optimal performance and the corresponding actuator location of the approximating sequence should converge to the exact optimal performance and location. Conditions for this convergence in the case of ℋ∞-control are provided. The results are illustrated with an example.