Linear-Quadratic Optimal Actuator Location

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 linear quadratic performance. Two types of cost are considered; the choice depends on whether the response to the worst initial condition is to be minimized; or whether the initial condition is regarded as random. In practice, approximations are used in controller design and thus in selection of the actuator locations. The optimal cost and location of the approximating sequence should converge to the exact optimal cost and location. In this work conditions for this convergence are given in the case of linear quadratic control. Examples are provided to illustrate that convergence may fail when these conditions are not satisfied.