Robustness of Controllability for Finite Dimensional Approximations of Distributed Parameter Systems

摘要

The nature in which controllability properties of an infinite dimensional distributed parameter system are inherited by various standard finite dimensional approximation schemes is investigated. This question arises when using numerical approximation schemes such as finite element, Galerkin, or finite difference schemes to approximate the original infinite dimensional model. A measure of robustness of controllability for the finite dimensional approximation scheme is given. An example in terms of the heat equation with distributed control illustrates the main ideas and difficulties. (KR)