Exact and Approximate Controllability for Distributed Parameter Systems
A Numerical Approach

A thorough mathematical analysis of controllability problems with a detailed investigation of methods for solving them numerically.

Roland Glowinski (Author), Jacques-Louis Lions (Author), Jiwen He (Author)

9780521885720, Cambridge University Press

Hardback, published 20 March 2008

470 pages, 51 b/w illus. 10 colour illus. 20 tables
24 x 16.5 x 3 cm, 0.816 kg

"The book definitely has the perfume of those that Lions wrote during his prolific career. My congratulations to his two coworkers for having completed this task that reminded incomplete when he passed away in 2001. This book definitely fills a gap in the existing in literature on control and numerics of PDS, and I am sure it will influence future research in this area."
Enrique Zuazua, Mathematical Reviews

The behaviour of systems occurring in real life is often modelled by partial differential equations. This book investigates how a user or observer can influence the behaviour of such 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 Part I of the book the authors discuss the mathematics and numerics relating to the controllability of systems modelled by linear and non-linear diffusion equations; Part II is dedicated to the controllability of vibrating systems, typical ones being those modelled by linear wave equations; finally, Part III covers flow control for systems governed by the Navier-Stokes equations modelling 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.

Preface
Introduction
Part I. Diffusion Models: 1. Distributed and point-wise control for linear diffusion equations
2. Boundary control
3. Control of the Stokes system
4. Control of nonlinear diffusion systems
5. Dynamic programming for linear diffusion equations
Part II. Wave Models: 6. Wave equations
7. Helmholtz equation
8. Coupled systems
Part III. Flow Control: 9. Optimal control of Navier-Stokes equations: drag reduction
Epilogue
Further acknowledgements
References.

Subject Areas: Numerical analysis [PBKS]