Representation and control of infinite dimensional systems

✍ Scribed by Bensoussan A., et al.

• Publisher: Birkhauser
• Year: 2007
• Tongue: English
• Leaves: 603
• Series: Systems & Control: Foundations & Applications
• Edition: 2ed
• Category: Library

✦ Synopsis

This unified, revised second edition of a two-volume set is a self-contained account of quadratic cost optimal control for a large class of infinite-dimensional systems. The original editions received outstanding reviews, yet this new edition is more concise and self-contained. New material has been added to reflect the growth in the field over the past decade. There is a unique chapter on semigroup theory of linear operators that brings together advanced concepts and techniques which are usually treated independently. The material on delay systems and structural operators has not yet appeared anywhere in book form.

✦ Table of Contents

Preface to the Second Edition......Page 8
Preface to Volume I of the First Edition......Page 12
Preface to Volume II of the First Edition......Page 16
Contents......Page 20
List of Figures......Page 28
1Scopeofthebook......Page 29
2 From .nite to in.nite dimensional sytems......Page 30
Part I Finite Dimensional Linear Control Dynamical Systems......Page 39
2 Controllability, observability, stabilizability, and detectability......Page 41
3Optimalcontrol......Page 58
4 A glimpse into......Page 63
5 Dissipative systems......Page 67
6 Final remarks......Page 72
1 Introduction......Page 75
2 De.nitions, notation, and preliminary results......Page 78
3 Saddle point and coupled state–adjoint state system......Page 82
4 Finite open loop lower value......Page 84
5Finiteopenloopvalueandopenloopsaddlepoint......Page 96
6 Riccati di.erential equation in the open loop saddle point case......Page 97
7 Riccati di.erential equation and open/closed loop upper/lower value of the game......Page 109
Part II Representation of In.nite Dimensional Linear Control Dynamical Systems......Page 113
1Notation......Page 115
2 Linear evolution equations and strongly continuous semigroups......Page 116
3 Nonhomogeneous linear evolution equations......Page 156
4 Interpolation spaces......Page 182
5 Fractional powers of dissipative operators......Page 195
6 Interpolation spaces and domains of fractional powers of an operator......Page 197
1 Variational di.erential equations......Page 201
2 Method of Transposition......Page 216
3 Second order problems......Page 226
1 Complements on semigroups......Page 229
2 Complements on analytic semigroups......Page 234
3 Unbounded control and observation operators......Page 238
4 Time-invariant variational parabolic systems......Page 250
1 Introduction......Page 257
2 Examples and orientation......Page 259
3 Existence theorems for Lipschitzian systems......Page 268
4 State space theory of linear time-invariant systems......Page 280
5 State space theory of linear control systems......Page 307
6 State space theory of linear control systems with observation......Page 325
Part III Qualitative Properties of In.nite Dimensional Linear Control Dynamical Systems......Page 339
1 Introduction......Page 341
2 Main de.nitions......Page 345
3 Criteria for approximate and exact controllability......Page 350
4 Finite dimensional control space......Page 353
5 Controllability for the heat equation......Page 358
6 Controllability for skew-symmetric operators......Page 367
7 General framework: skew-symmetric operators......Page 390
8 Exact controllability of hyperbolic equations......Page 395
Part IV Quadratic Optimal Control: Finite Time Horizon......Page 411
1 Introduction and setting of the problem......Page 413
2 Solution of the Riccati equation......Page 414
3 Strict and classical solutions of the Riccati equation......Page 425
4 The case of the unbounded observation......Page 433
5Thecasewhen......Page 435
6 The linear quadratic control problem with .nite horizon......Page 436
7 Some generalizations and complements......Page 440
8 Examples of controlled systems......Page 446
1 Introduction......Page 459
2 Riccati equation......Page 466
3 Dynamic programming......Page 482
1 Introduction......Page 487
2 Riccati equation......Page 490
3 Dynamic programming......Page 491
4 Examples of controlled hyperbolic systems......Page 494
5 Some result for general semigroups......Page 499
Part V Quadratic Optimal Control: In.nite Time Horizon......Page 504
1 Introduction and setting of the problem......Page 507
2 The algebraic Riccati equation......Page 508
3 Solution of the control problem......Page 514
4 Qualitative properties of the solutions of the Riccati equation......Page 521
5 Some generalizations and complements......Page 533
6 Examples of controlled systems......Page 541
1 Introduction and setting of the problem......Page 545
2 The algebraic Riccati equation......Page 546
3 Dynamic programming......Page 549
1 Introduction and setting of the problem......Page 557
2Mainresults......Page 558
3 Some result for general semigroups......Page 562
A An Isomorphism Result......Page 565
References......Page 569
Index......Page 597