Exact and approximate controllability for distributed parameter systems : a numerical approach /
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| Author / Creator: | Glowinski, R. |
|---|---|
| Imprint: | Cambridge, UK ; New York : Cambridge University Press, 2008. |
| Description: | xii, 458 p. : ill. ; 24 cm. |
| Language: | English |
| Series: | Encyclopedia of mathematics and its applications ; 117 |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/7095575 |
Table of Contents:
- Preface
- Introduction
- I.1. What it is all about?
- I.2. Motivation
- I.3. Topologies and numerical methods
- I.4. Choice of the control
- I.5. Relaxation of the controllability notion
- I.6. Various remarks
- Part I. Diffusion Models
- 1. Distributed and pointwise control for linear diffusion equations
- 1.1. First example
- 1.2. Approximate controllability
- 1.3. Formulation of the approximate controllability problem
- 1.4. Dual problem
- 1.5. Direct solution to the dual problem
- 1.6. Penalty arguments
- 1.7. L[superscript infinity] cost functions and bang-bang controls
- 1.8. Numerical methods
- 1.9. Relaxation of controllability
- 1.10. Pointwise control
- 1.11. Further remarks (I): Additional constraints on the state function
- 1.12. Further remarks (II): A bisection based memory saving method for the solution of time dependent control problems by adjoint equation based methodologies
- 1.13. Further remarks (III): A brief introduction to Riccati equations based control methods
- 2. Boundary control
- 2.1. Dirichlet control (I): Formulation of the control problem
- 2.2. Dirichlet control (II): Optimality conditions and dual formulations
- 2.3. Dirichlet control (III): Iterative solution of the control problems
- 2.4. Dirichlet control (IV): Approximation of the control problems
- 2.5. Dirichlet control (V): Iterative solution of the fully discrete dual problem (2.124)
- 2.6. Dirichlet control (VI): Numerical experiments
- 2.7. Neumann control (I): Formulation of the control problems and synopsis
- 2.8. Neumann control (II): Optimality conditions and dual formulations
- 2.9. Neumann control (III): Conjugate gradient solution of the dual problem (2.192)
- 2.10. Neumann control (IV): Iterative solution of the dual problem (2.208), (2.209)
- 2.11. Neumann control of unstable parabolic systems: a numerical approach
- 2.12. Closed-loop Neumann control of unstable parabolic systems via the Riccati equation approach
- 3. Control of the Stokes system
- 3.1. Generalities. Synopsis
- 3.2. Formulation of the Stokes system. A fundamental controllability result
- 3.3. Two approximate controllability problems
- 3.4. Optimality conditions and dual problems
- 3.5. Iterative solution of the control problem (3.19)
- 3.6. Time discretization of the control problem (3.19)
- 3.7. Numerical experiments
- 4. Control of nonlinear diffusion systems
- 4.1. Generalities. Synopsis
- 4.2. Example of a noncontrollable nonlinear system
- 4.3. Pointwise control of the viscous Burgers equation
- 4.4. On the controllability and the stabilization of the Kuramoto-Sivashinsky equation in one space dimension
- 5. Dynamic programming for linear diffusion equations
- 5.1. Introduction. Synopsis
- 5.2. Derivation of the Hamilton-Jacobi-Bellman equation
- 5.3. Some remarks
- Part II. Wave Models
- 6. Wave equations
- 6.1. Wave equations: Dirichlet boundary control
- 6.2. Approximate controllability
- 6.3. Formulation of the approximate controllability problem
- 6.4. Dual problems
- 6.5. Direct solution of the dual problem
- 6.6. Exact controllability and new functional spaces
- 6.7. On the structure of space E
- 6.8. Numerical methods for the Dirichlet boundary controllability of the wave equation
- 6.9. Experimental validation of the filtering procedure of Section 6.8.7 via the solution of the test problem of Section 6.8.5
- 6.10. Some references on alternative approximation methods
- 6.11. Other boundary controls
- 6.12. Distributed controls for wave equations
- 6.13. Dynamic programming
- 7. On the application of controllability methods to the solution of the Helmholtz equation at large wave numbers
- 7.1. Introduction
- 7.2. The Helmholtz equation and its equivalent wave problem
- 7.3. Exact controllability methods for the calculation of time-periodic solutions to the wave equation
- 7.4. Least-squares formulation of the problem (7.8)-(7.11)
- 7.5. Calculation of J'
- 7.6. Conjugate gradient solution of the least-squares problem (7.14)
- 7.7. A finite element-finite difference implementation
- 7.8. Numerical experiments
- 7.9. Further comments. Description of a mixed formulation based variant of the controllability method
- 7.10. A final comment
- 8. Other wave and vibration problems. Coupled systems
- 8.1. Generalities and further references
- 8.2. Coupled Systems (I): a problem from thermo-elasticity
- 8.3. Coupled systems (II): Other systems
- Part III. Flow Control
- 9. Optimal control of systems modelled by the Navier-Stokes equations: Application to drag reduction
- 9.1. Introduction. Synopsis
- 9.2. Formulation of the control problem
- 9.3. Time discretization of the control problem
- 9.4. Full discretization of the control problem
- 9.5. Gradient calculation
- 9.6. A BFGS algorithm for solving the discrete control problem
- 9.7. Validation of the flow simulator
- 9.8. Active control by rotation
- 9.9. Active control by blowing and suction
- 9.10. Further comments on flow control and conclusion
- Epilogue
- Further Acknowledgements
- References
- Index of names
- Index of subjects
