| Preface | p. xi |
| Introduction | p. 1 |
| What it is all about? | p. 1 |
| Motivation | p. 2 |
| Topologies and numerical methods | p. 3 |
| Choice of the control | p. 4 |
| Relaxation of the controllability notion | p. 4 |
| Various remarks | p. 5 |
| Diffusion Models | |
| Distributed and pointwise control for linear diffusion equations | p. 9 |
| First example | p. 9 |
| Approximate controllability | p. 12 |
| Formulation of the approximate controllability problem | p. 14 |
| Dual problem | p. 15 |
| Direct solution to the dual problem | p. 17 |
| Penalty arguments | p. 19 |
| L[superscript infinity] cost functions and bang-bang controls | p. 22 |
| Numerical methods | p. 28 |
| Relaxation of controllability | p. 57 |
| Pointwise control | p. 62 |
| Further remarks (I): Additional constraints on the state function | p. 96 |
| Further remarks (II): A bisection based memory saving method for the solution of time dependent control problems by adjoint equation based methodologies | p. 112 |
| Further remarks (III): A brief introduction to Riccati equations based control methods | p. 117 |
| Boundary control | p. 124 |
| Dirichlet control (I): Formulation of the control problem | p. 124 |
| Dirichlet control (II): Optimality conditions and dual formulations | p. 126 |
| Dirichlet control (III): Iterative solution of the control problems | p. 128 |
| Dirichlet control (IV): Approximation of the control problems | p. 133 |
| Dirichlet control (V): Iterative solution of the fully discrete dual problem (2.124) | p. 143 |
| Dirichlet control (VI): Numerical experiments | p. 146 |
| Neumann control (I): Formulation of the control problems and synopsis | p. 155 |
| Neumann control (II): Optimality conditions and dual formulations | p. 163 |
| Neumann control (III): Conjugate gradient solution of the dual problem (2.192) | p. 176 |
| Neumann control (IV): Iterative solution of the dual problem (2.208), (2.209) | p. 178 |
| Neumann control of unstable parabolic systems: a numerical approach | p. 178 |
| Closed-loop Neumann control of unstable parabolic systems via the Riccati equation approach | p. 223 |
| Control of the Stokes system | p. 231 |
| Generalities. Synopsis | p. 231 |
| Formulation of the Stokes system. A fundamental controllability result | p. 231 |
| Two approximate controllability problems | p. 234 |
| Optimality conditions and dual problems | p. 234 |
| Iterative solution of the control problem (3.19) | p. 236 |
| Time discretization of the control problem (3.19) | p. 238 |
| Numerical experiments | p. 239 |
| Control of nonlinear diffusion systems | p. 243 |
| Generalities. Synopsis | p. 243 |
| Example of a noncontrollable nonlinear system | p. 243 |
| Pointwise control of the viscous Burgers equation | p. 245 |
| On the controllability and the stabilization of the Kuramoto-Sivashinsky equation in one space dimension | p. 259 |
| Dynamic programming for linear diffusion equations | p. 277 |
| Introduction. Synopsis | p. 277 |
| Derivation of the Hamilton-Jacobi-Bellman equation | p. 278 |
| Some remarks | p. 279 |
| Wave Models | |
| Wave equations | p. 283 |
| Wave equations: Dirichlet boundary control | p. 283 |
| Approximate controllability | p. 285 |
| Formulation of the approximate controllability problem | p. 286 |
| Dual problems | p. 287 |
| Direct solution of the dual problem | p. 288 |
| Exact controllability and new functional spaces | p. 289 |
| On the structure of space E | p. 291 |
| Numerical methods for the Dirichlet boundary controllability of the wave equation | p. 291 |
| Experimental validation of the filtering procedure of Section 6.8.7 via the solution of the test problem of Section 6.8.5 | p. 315 |
| Some references on alternative approximation methods | p. 319 |
| Other boundary controls | p. 320 |
| Distributed controls for wave equations | p. 328 |
| Dynamic programming | p. 329 |
| On the application of controllability methods to the solution of the Helmholtz equation at large wave numbers | p. 332 |
| Introduction | p. 332 |
| The Helmholtz equation and its equivalent wave problem | p. 332 |
| Exact controllability methods for the calculation of time-periodic solutions to the wave equation | p. 334 |
| Least-squares formulation of the problem (7.8)-(7.11) | p. 334 |
| Calculation of J' | p. 336 |
| Conjugate gradient solution of the least-squares problem (7.14) | p. 337 |
| A finite element-finite difference implementation | p. 340 |
| Numerical experiments | p. 341 |
| Further comments. Description of a mixed formulation based variant of the controllability method | p. 349 |
| A final comment | p. 355 |
| Other wave and vibration problems. Coupled systems | p. 356 |
| Generalities and further references | p. 356 |
| Coupled Systems (I): a problem from thermo-elasticity | p. 359 |
| Coupled systems (II): Other systems | p. 367 |
| Flow Control | |
| Optimal control of systems modelled by the Navier-Stokes equations: Application to drag reduction | p. 371 |
| Introduction. Synopsis | p. 371 |
| Formulation of the control problem | p. 373 |
| Time discretization of the control problem | p. 377 |
| Full discretization of the control problem | p. 379 |
| Gradient calculation | p. 384 |
| A BFGS algorithm for solving the discrete control problem | p. 388 |
| Validation of the flow simulator | p. 389 |
| Active control by rotation | p. 394 |
| Active control by blowing and suction | p. 408 |
| Further comments on flow control and conclusion | p. 419 |
| Epilogue | p. 426 |
| Further Acknowledgements | p. 429 |
| References | p. 430 |
| Index of names | p. 450 |
| Index of subjects | p. 454 |
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