【2019新书】Turnpike Conditions in Infinite Dimensional Optimal Control [推广有奖]

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Turnpike Conditions in Infinite Dimensional Optimal Control
by Alexander J. Zaslavski (Author)

About the Author
Alexander J. Zaslavski is a Senior Researcher in the Department of Mathematics at Technion-Israel Institute of Technology in Haifa. He has published over one hundred journal articles, and has authored books including Optimization on Metric and Normed Spaces (Springer, 2010) , etc.

About this book
This book provides a comprehensive study of turnpike phenomenon arising in optimal control theory. The focus is on individual (non-generic) turnpike results which are both mathematically significant and have numerous applications in engineering and economic theory. All results obtained in the book are new. New approaches, techniques, and methods are rigorously presented and utilize research from finite-dimensional variational problems and discrete-time optimal control problems to find the necessary conditions for the turnpike phenomenon in infinite dimensional spaces.
The semigroup approach is employed in the discussion as well as PDE descriptions of continuous-time dynamics. The main results on sufficient and necessary conditions for the turnpike property are completely proved and the numerous examples support the material for the broad spectrum of experts. Mathematicians interested in the calculus of variations, optimal control and in applied functional analysis will find this book a useful guide to the turnpike phenomenon in infinite dimensional spaces.  Experts in economic and engineering modeling as well as graduate students will also benefit from the developed techniques and obtained results.

Brief contents
1 Introduction 1
1. 1 Banach Space Valued Functions 1
1. 2 Unbounded Operators 3
1.3 C 0 Semigroup  4
1. 4 Evolution Equations 6
1.5 C 0 Groups  7
1. 6 Notation 8
1. 7 Admissible Control Operators 9
1. 8 Examples 15
1. 9 Turnpike Property for Variational Problems 20
2 Discrete-Time Autonomous Problems 25
2. 1 Preliminaries and Main Results 25
2. 2 Lower Semicontinuity Property 31
2. 3 Perturbed Problems 35
2. 4 A Subclass of Problems 36
2. 5 Structure of Solutions in the Regions Close to the Endpoints 42
2. 6 Examples 45
2. 7 Auxiliary Results for Theorem 2. 1 49
2. 8 Proofs of Theorems 2. 1–2. 4 52
2. 9 Proof of Theorem 2. 9 55
2. 10 An Auxiliary Result for Theorem 2. 10 63
2. 11 Proof of Theorem 2. 10 65
2. 12 Proof of Proposition 2. 12 70
2. 13 Auxiliary Results for Theorems 2. 13 and 2. 14 71
2. 14 Proofs of Theorems 2. 13 and 2. 14 77
2. 15 Proofs of Theorems 2. 15–2. 17 80
2. 16 Proof of Theorem 2. 21 85
2. 17 Proofs of Propositions 2. 25–2. 27, 2. 29, and 2. 31 86
2. 18 Proof of Proposition 2. 37 94
2. 19 Auxiliary Results for Theorems 2. 38 and 2. 39 96
2. 20 Proofs of Theorems 2. 38 and 2. 39 97
2. 21 Proofs of Theorem 2. 40 and 2. 41 102
2. 22 The First Bolza Problem 104
2. 23 Proof of Theorem 2. 63 108
2. 24 Proof of Theorem 2. 66 110
2. 25 Proof of Proposition 2. 69 115
2. 26 The Second Bolza Problem 117
2. 27 Proof of Theorem 2. 70 119
2. 28 Proof of Theorem 2. 71 120
2. 29 Proof of Proposition 2. 73 127
3 Discrete-Time Nonautonomous Problems on the Half-Axis 131
3. 1 Preliminaries and Main Results 131
3. 2 The Boundedness Results 134
3. 3 Turnpike Properties 136
3. 4 Lower Semicontinuity Property and Infinite Horizon Problems 142
3. 5 Perturbed Problems 145
3. 6 Examples 148
3. 7 Auxiliary Results for Theorems 3. 1 and 3. 2 153
3. 8 Proofs of Theorems 3. 1–3. 5 156
3. 9 An Auxiliary Result for Theorem 3. 17 158
3. 10 Proof of Theorem 3. 17 159
3. 11 An Auxiliary Result 165
3. 12 Proof of Theorem 3. 18 168
3. 13 Auxiliary Results for Theorems 3. 19 172
3. 14 Proofs of Theorems 3. 19 and 3. 20 179
3. 15 An Auxiliary Result for Theorem 3. 24 183
3. 16 Proof of Theorem 3. 24 184
3. 17 Proof of Theorem 3. 26 191
4 Discrete-Time Nonautonomous Problems on Axis 197
4. 1 Preliminaries and Main Results 197
4. 2 Boundedness Results 200
4. 3 Turnpike Results 202
4. 4 Perturbed Problems 207
4. 5 Auxiliary Results for Theorems 4. 1 and 4. 2 208
4. 6 Proof of Theorems 4. 1 and 4. 2 211
4. 7 Proofs of Propositions 4. 10, 4. 12 and Theorems 4. 3–4. 5 213
4. 8 Auxiliary Results for Theorem 4. 7 215
4. 9 STP Implies (P1)–(P3) 219
4. 10 (P1)–(P3) Imply STP 229
4. 11 Proof of Theorem 4. 8 253
4. 12 Proof of Theorem 4. 13 255
4. 13 Proof of Theorem 4. 16 262
5 Continuous-Time Autonomous Problems 269
5. 1 Preliminaries 269
5. 2 Boundedness Results 275
5. 3 Turnpike Results 277
5. 4 Lower Semicontinuity Property 280
5. 5 Perturbed Problems 282
5.6 The Triplet ( f , − A , − G )  283
5. 7 Auxiliary Results for Theorem 5. 1 288
5. 8 Proofs of Theorems 5. 1–5. 4 294
5. 9 Proofs of Theorems 5. 6–5. 9 299
5. 10 Proofs of Theorems 5. 11 and 5. 12 303
5. 11 Proof of Theorem 5. 13 304
5. 12 An Auxiliary Result 309
5. 13 Proof of Theorem 5. 14 311
5. 14 Proof of Proposition 5. 16 315
5. 15 Proof of Proposition 5. 18 316
5. 16 Auxiliary Results for Theorems 5. 19 and 5. 20 318
5. 17 Proofs of Theorems 5. 19 and 5. 20 322
5. 18 Proofs of Theorems 5. 21–5. 23 325
5. 19 Proof of Proposition 5. 27 329
5. 20 Proof of Theorem 5. 28 336
5. 21 Auxiliary Results 337
5. 22 Structure of Solutions in the Regions Close to the Endpoints 348
5. 23 Auxiliary Results for Theorems 5. 58–5. 61 350
5. 24 Proofs of Theorems 5. 58 and 5. 59 351
5. 25 Proofs of Theorems 5. 60 and 5. 61 355
5. 26 The First Bolza Problem 357
5. 27 Proof of Theorem 5. 68 361
5. 28 Proof of Theorem 5. 71 362
5. 29 Proof of Proposition 5. 74 367
5. 30 The Second Bolza Problem 369
5. 31 Proof of Theorem 5. 75 371
5. 32 Proof of Theorem 5. 76 372
5. 33 Proof of Proposition 5. 78 378
5. 34 Examples 381
5. 35 Exercises for Chapter 5 384
6 Continuous-Time Nonautonomous Problems on the Half-Axis 385
6. 1 Preliminaries 385
6. 2 Boundedness Results 391
6. 3 Turnpike Results 393
6. 4 Lower Semicontinuity Property 400
6. 5 Perturbed Problems 402
6. 6 Auxiliary Results for Theorems 6. 2 and 6. 3 403
6. 7 Proofs of Theorems 6. 2 and 6. 3 410
6. 8 Proofs of Theorems 6. 4–6. 10 413
6. 9 Proof of Theorem 6. 22 419
6. 10 An Auxiliary Result for Theorem 6. 23 424
6. 11 Proof of Theorem 6. 23 426
6. 12 An Auxiliary Result 431
6. 13 Proof of Proposition 6. 27 432
6. 14 Auxiliary Results for Theorems 6. 28 and 6. 29 440
6. 15 Proofs of Theorems 6. 28 and 6. 29 444
6. 16 Auxiliary Results for Theorem 6. 33 447
6. 17 Proof of Theorem 6. 33 454
6. 18 Proof of Theorem 6. 35 469
6. 19 Examples 471
6. 20 Exercises for Chapter 6 478
7 Continuous-Time Nonautonomous Problems on Axis 479
7. 1 Preliminaries 479
7. 2 Boundedness Results 482
7. 3 Turnpike Results 483
7. 4 Perturbed Problems 487
7. 5 Auxiliary Results 488
7. 6 Proofs of Theorems 7. 2–7. 5 497
7. 7 Auxiliary Results 502
7. 8 STP Implies (P1), (P2), and (P3) 505
7. 9 An Auxiliary Result 513
7. 10 The Main Lemma 516
7. 11 Completion of the Proof of Theorem 7. 8 536
7. 12 An Auxiliary Result for Theorem 7. 9 537
7. 13 Proofs of Propositions 7. 11 and 7. 13 539
7. 14 Proofs of Theorems 7. 9 and 7. 14 540
7. 15 Auxiliary Results for Theorem 7. 15 548
7. 16 Proof of Theorems 7. 15 552
7. 17 Proof of Theorem 7. 16 555
7. 18 An Example 561
References 563
Index 569

Series: Springer Optimization and Its Applications (Book 148)
Pages: 570 pages
Publisher: Springer; 1st ed. 2019 edition (September 11, 2019)
Language: English
ISBN-10: 3030201775
ISBN-13: 978-3030201777

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