Exact and approximate controllability for distributed parameter systems : a numerical approach
著者
書誌事項
Exact and approximate controllability for distributed parameter systems : a numerical approach
（Encyclopedia of mathematics and its applications / edited by G.-C. Rota, 117）
Cambridge University Press, 2008
- : hardback
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注記
Includes bibliographical references (p. [430]-449) and indexes
内容説明・目次
内容説明
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.
目次
- 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.
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