Exact and Approximate Controllability for Distributed Parameter Systems

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 those modeled by linear wave equations; and finally, part three covers flow control for systems governed by the Navier-Stokes equations modeling incompressible viscous flow. The book is accessible to graduate students in applied and computational mathematics, engineering and physics; it will also be of use to more advanced practitioners.

• Computationally oriented with a thorough discussion of the solution methods employed in the various chapters (finite element methods, conjugate gradient algorithms and more)
• Blends mathematical analysis and numerical analysis and illustrates with a large variety of numerical experiments
• One of the few books on controllability issues for systems modelled by partial differential equations from mechanics and physics, a hot topic at the moment