Optimal Actuator Location for Diffusion Equation with Neumann Boundary Control

Abstract

This paper is concerned with optimal actuator location for a class of diffusion equations with boundary control. The problem of optimal actuator location based on a linear quadratic cost in case of the worst initial condition is formulated. This leads to a cost involving the operator norm of the Riccati operator. The existence of optimal locations within the uniform operator norm is guaranteed. A Galerkin-based algorithm for approximating the optimal locations, and the convergence of the approximation of the optimal locations is also presented.