This book investigates how a user or observer can influence the behavior of systems mathematically and computationally. A thorough mathematical analysis of controllability problems is combined with a detailed investigation of methods used to solve them numerically; these methods being validated by the results of numerical experiments. In the first part of the book, the authors discuss the mathematics and numerics relating to the controllability of systems modeled by linear and non-linear diffusion equations; Part two is dedicated to the controllability of vibrating systems, typical ones being...