Turnpike conditions in infinite dimensional optimal control

Preface......Page 5
Contents......Page 7
 1.1 Banach Space Valued Functions......Page 11
 1.2 Unbounded Operators......Page 13
 1.3 C0 Semigroup......Page 14
 1.4 Evolution Equations......Page 16
 1.5 C0 Groups......Page 17
 1.6 Notation......Page 18
 1.7 Admissible Control Operators......Page 19
 1.8 Examples......Page 25
 1.9 Turnpike Property for Variational Problems......Page 30
 2.1 Preliminaries and Main Results......Page 35
 2.2 Lower Semicontinuity Property......Page 41
 2.3 Perturbed Problems......Page 45
 2.4 A Subclass of Problems......Page 46
 2.5 Structure of Solutions in the Regions Close to the Endpoints......Page 52
 2.6 Examples......Page 55
 2.7 Auxiliary Results for Theorem 2.1......Page 59
 2.8 Proofs of Theorems 2.1–2.4......Page 62
 2.9 Proof of Theorem 2.9......Page 65
 2.10 An Auxiliary Result for Theorem 2.10......Page 73
 2.11 Proof of Theorem 2.10......Page 75
 2.12 Proof of Proposition 2.12......Page 80
 2.13 Auxiliary Results for Theorems 2.13 and 2.14......Page 81
 2.14 Proofs of Theorems 2.13 and 2.14......Page 87
 2.15 Proofs of Theorems 2.15–2.17......Page 90
 2.16 Proof of Theorem 2.21......Page 95
 2.17 Proofs of Propositions 2.25–2.27, 2.29, and 2.31......Page 96
 2.18 Proof of Proposition 2.37......Page 104
 2.19 Auxiliary Results for Theorems 2.38 and 2.39......Page 106
 2.20 Proofs of Theorems 2.38 and 2.39......Page 107
 2.21 Proofs of Theorem 2.40 and 2.41......Page 112
 2.22 The First Bolza Problem......Page 114
 2.23 Proof of Theorem 2.63......Page 118
 2.24 Proof of Theorem 2.66......Page 120
 2.25 Proof of Proposition 2.69......Page 125
 2.26 The Second Bolza Problem......Page 127
 2.27 Proof of Theorem 2.70......Page 129
 2.28 Proof of Theorem 2.71......Page 130
 2.29 Proof of Proposition 2.73......Page 137
 3.1 Preliminaries and Main Results......Page 141
 3.2 The Boundedness Results......Page 144
 3.3 Turnpike Properties......Page 146
 3.4 Lower Semicontinuity Property and Infinite Horizon Problems......Page 152
 3.5 Perturbed Problems......Page 155
 3.6 Examples......Page 158
 3.7 Auxiliary Results for Theorems 3.1 and 3.2......Page 163
 3.8 Proofs of Theorems 3.1–3.5......Page 166
 3.9 An Auxiliary Result for Theorem 3.17......Page 168
 3.10 Proof of Theorem 3.17......Page 169
 3.11 An Auxiliary Result......Page 175
 3.12 Proof of Theorem 3.18......Page 178
 3.13 Auxiliary Results for Theorems 3.19......Page 182
 3.14 Proofs of Theorems 3.19 and 3.20......Page 189
 3.15 An Auxiliary Result for Theorem 3.24......Page 193
 3.16 Proof of Theorem 3.24......Page 194
 3.17 Proof of Theorem 3.26......Page 201
 4.1 Preliminaries and Main Results......Page 206
 4.2 Boundedness Results......Page 209
 4.3 Turnpike Results......Page 211
 4.4 Perturbed Problems......Page 216
 4.5 Auxiliary Results for Theorems 4.1 and 4.2......Page 217
 4.6 Proof of Theorems 4.1 and 4.2......Page 220
 4.7 Proofs of Propositions 4.10, 4.12 and Theorems 4.3–4.5......Page 222
 4.8 Auxiliary Results for Theorem 4.7......Page 224
 4.9 STP Implies (P1)–(P3)......Page 228
 4.10 (P1)–(P3) Imply STP......Page 238
 4.11 Proof of Theorem 4.8......Page 262
 4.12 Proof of Theorem 4.13......Page 264
 4.13 Proof of Theorem 4.16......Page 271
 5.1 Preliminaries......Page 277
 5.2 Boundedness Results......Page 283
 5.3 Turnpike Results......Page 285
 5.4 Lower Semicontinuity Property......Page 288
 5.5 Perturbed Problems......Page 290
 5.6 The Triplet (f,-A,-G)......Page 291
 5.7 Auxiliary Results for Theorem 5.1......Page 296
 5.8 Proofs of Theorems 5.1–5.4......Page 302
 5.9 Proofs of Theorems 5.6–5.9......Page 307
 5.10 Proofs of Theorems 5.11 and 5.12......Page 311
 5.11 Proof of Theorem 5.13......Page 312
 5.12 An Auxiliary Result......Page 317
 5.13 Proof of Theorem 5.14......Page 319
 5.14 Proof of Proposition 5.16......Page 323
 5.15 Proof of Proposition 5.18......Page 324
 5.16 Auxiliary Results for Theorems 5.19 and 5.20......Page 326
 5.17 Proofs of Theorems 5.19 and 5.20......Page 330
 5.18 Proofs of Theorems 5.21–5.23......Page 333
 5.19 Proof of Proposition 5.27......Page 337
 5.20 Proof of Theorem 5.28......Page 344
 5.21 Auxiliary Results......Page 345
 5.22 Structure of Solutions in the Regions Close to the Endpoints......Page 356
 5.23 Auxiliary Results for Theorems 5.58–5.61......Page 358
 5.24 Proofs of Theorems 5.58 and 5.59......Page 359
 5.25 Proofs of Theorems 5.60 and 5.61......Page 363
 5.26 The First Bolza Problem......Page 365
 5.27 Proof of Theorem 5.68......Page 369
 5.28 Proof of Theorem 5.71......Page 370
 5.29 Proof of Proposition 5.74......Page 375
 5.30 The Second Bolza Problem......Page 377
 5.31 Proof of Theorem 5.75......Page 379
 5.32 Proof of Theorem 5.76......Page 380
 5.33 Proof of Proposition 5.78......Page 386
 5.34 Examples......Page 389
 5.35 Exercises for Chapter 5......Page 392
 6.1 Preliminaries......Page 393
 6.2 Boundedness Results......Page 399
 6.3 Turnpike Results......Page 401
 6.4 Lower Semicontinuity Property......Page 408
 6.5 Perturbed Problems......Page 410
 6.6 Auxiliary Results for Theorems 6.2 and 6.3......Page 411
 6.7 Proofs of Theorems 6.2 and 6.3......Page 418
 6.8 Proofs of Theorems 6.4–6.10......Page 421
 6.9 Proof of Theorem 6.22......Page 427
 6.10 An Auxiliary Result for Theorem 6.23......Page 432
 6.11 Proof of Theorem 6.23......Page 434
 6.12 An Auxiliary Result......Page 439
 6.13 Proof of Proposition 6.27......Page 440
 6.14 Auxiliary Results for Theorems 6.28 and 6.29......Page 448
 6.15 Proofs of Theorems 6.28 and 6.29......Page 452
 6.16 Auxiliary Results for Theorem 6.33......Page 455
 6.17 Proof of Theorem 6.33......Page 462
 6.18 Proof of Theorem 6.35......Page 477
 6.19 Examples......Page 479
 6.20 Exercises for Chapter 6......Page 486
 7.1 Preliminaries......Page 487
 7.2 Boundedness Results......Page 490
 7.3 Turnpike Results......Page 491
 7.4 Perturbed Problems......Page 495
 7.5 Auxiliary Results......Page 496
 7.6 Proofs of Theorems 7.2–7.5......Page 505
 7.7 Auxiliary Results......Page 510
 7.8 STP Implies (P1), (P2), and (P3)......Page 513
 7.9 An Auxiliary Result......Page 521
 7.10 The Main Lemma......Page 524
 7.11 Completion of the Proof of Theorem 7.8......Page 544
 7.12 An Auxiliary Result for Theorem 7.9......Page 545
 7.13 Proofs of Propositions 7.11 and 7.13......Page 547
 7.14 Proofs of Theorems 7.9 and 7.14......Page 548
 7.15 Auxiliary Results for Theorem 7.15......Page 556
 7.16 Proof of Theorems 7.15......Page 560
 7.17 Proof of Theorem 7.16......Page 563
 7.18 An Example......Page 569
References......Page 571
Index......Page 577