Summer school on mathematical control theory

Part I......Page 1
Summer School on Mathematical Control Theory, 3-28 September 2001, ICTP, Trieste, Italy......Page 2
ISBN 929500311X......Page 3
Preface......Page 4
Contents......Page 6
Introduction......Page 8
Classical Control Theory......Page 10
Contents......Page 12
0 Introduction......Page 14
1 Controllability and Observability......Page 18
2 Stability and stabilizability......Page 37
3 Linear quadratic problem......Page 49
References......Page 64
Linear Quadratic Control Theory for Infinite Dimensional Systems......Page 68
Contents......Page 70
1 Control infinite horizon......Page 72
2 Control in infinite horizon......Page 84
3 Examples and generalizations......Page 92
APPENDICES A Linear Semigroups Theory......Page 99
B Contraction Principle......Page 111
Introduction to Geometric Nonlinear Control; Controllability and Lie Bracket......Page 116
Contents......Page 118
1 Controllability and Lie bracket......Page 120
2 Orbits, distributions, and foliations......Page 139
3 Controllability and accessibility......Page 152
4 Controllability and path approximation......Page 163
References......Page 177
Introduction to Geometric Nonlinear Control; Linearization, Observability, Decoupling......Page 178
Contents......Page 180
2 Feedback linearization: an introduction......Page 182
3 Equivalence of control systems......Page 190
4 Feedback linearization......Page 195
5 Observability......Page 205
6 Decoupling......Page 219
References......Page 227
The Combinatorics of Nonlinear Controllability and Noncommuting Flows......Page 232
Contents......Page 234
0 Organization and objectives......Page 236
1 Nonlinear controllability......Page 237
2 Series expansion, nilpotent approximating systems......Page 256
3 Combinatorics of words and free Lie algebras......Page 268
4 A primer on exponential product expansions......Page 291
Acknowledgments......Page 313
References......Page 315
Stability Analysis Based on Direct Liapunov Method......Page 322
Contents......Page 324
Introduction......Page 326
1 Unforced systems......Page 327
2 Stability and nonsmooth analysis......Page 334
3 Stabilization......Page 344
4 Control Liapunov functions......Page 353
Acknowledgments......Page 359
References......Page 360
Part II......Page 374
Introduction to Optimal Control Theory......Page 375
Contents......Page 377
1 Optimal control problem......Page 379
2 Pontryagin Maximum Principle......Page 382
3 Existence of Optimal controls......Page 392
4 Examples of optimal control problems......Page 396
5 Linear time-optimal problem......Page 411
6 Linear-quadratic problem......Page 424
Exercises......Page 435
References......Page 436
Value Function in Optimal Control......Page 439
Contents......Page 441
1 Preliminaries: Set-Valued Analysis......Page 443
2 Control Systems and Differential Inclusions......Page 472
3 Value Function of Mayer’s Problem......Page 486
4 Hamilton-Jacobi-Bellman Equation......Page 515
5 Value Function of Bolza Problem and Riccati Equations......Page 531
6 Hamilton-Jacobi-Bellman Equation for Problems under State-Constraints......Page 557
References......Page 573
Return Method: Some Applications to Flow Control......Page 579
Contents......Page 581
2 Return method......Page 583
3 Controllability of the Euler and Navier-Stokes equations......Page 590
4 Local controllability of a 1-D tank containing afluid modeled by the Saint-Venant equations......Page 601
5 Null asymptotic stabilizability of the 2-D Euler control system......Page 616
References......Page 622
Flat Systems......Page 629
Contents......Page 631
Introduction......Page 633
1 Equivalence and flatness......Page 636
2 Feedback design with equivalence......Page 648
3 Open problems and new perspectives......Page 662
4 A catalog of flat systems......Page 676
References......Page 686
Mass Balance Modelling of Bioprocesses......Page 693
Contents......Page 695
1 Introduction......Page 697
2 Principle of a bioreactor......Page 698
3 The mass balance modelling......Page 702
4 The mass balance models......Page 706
5 Modelling of the kinetics......Page 713
6 Model validation......Page 718
7 Mass balance models properties......Page 725
8 Conclusion......Page 730
Appendix A.Theoretical determination of the dimension of K......Page 731
References......Page 734
State Estimation for Bioprocesses......Page 737
Contents......Page 739
2 Notions on system observability......Page 741
3 Observers for linear systems......Page 746
4 High gain observers......Page 751
5 Observers for mass balance based systems......Page 757
6 interval observers......Page 764
7 Interval estimator for an activated sludge process......Page 768
8 Conclusion......Page 770
References......Page 773