دانلود کتاب Optimal control theory: applications to management science and economics

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Preface to Third Edition......Page 6
Preface to Second Edition......Page 8
Preface to First Edition......Page 11
Contents......Page 13
List of Figures......Page 20
List of Tables......Page 24
1 What Is Optimal Control Theory?......Page 25
1.1 Basic Concepts and Definitions......Page 26
1.2 Formulation of Simple Control Models......Page 28
1.3 History of Optimal Control Theory......Page 33
1.4 Notation and Concepts Used......Page 35
1.4.1 Differentiating Vectors and Matrices with Respect To Scalars......Page 36
1.4.2 Differentiating Scalars with Respect to Vectors......Page 37
1.4.3 Differentiating Vectors with Respect to Vectors......Page 38
1.4.5 Miscellany......Page 40
1.4.7 Concave and Convex Functions......Page 44
1.4.9 Saddle Point......Page 46
1.5 Plan of the Book......Page 47
2.1 Statement of the Problem......Page 51
2.1.2 Constraints......Page 52
2.1.4 The Optimal Control Problem......Page 53
2.2.1 The Hamilton-Jacobi-Bellman Equation......Page 56
2.2.2 Derivation of the Adjoint Equation......Page 60
2.2.3 The Maximum Principle......Page 63
2.2.4 Economic Interpretations of the Maximum Principle......Page 64
2.3 Simple Examples......Page 66
2.4 Sufficiency Conditions......Page 77
2.5 Solving a TPBVP by Using Excel......Page 81
3 The Maximum Principle: Mixed Inequality Constraints......Page 92
3.1 A Maximum Principle for Problems with Mixed Inequality Constraints......Page 93
3.2 Sufficiency Conditions......Page 102
3.3 Current-Value Formulation......Page 103
3.4 Transversality Conditions: Special Cases......Page 109
3.5 Free Terminal Time Problems......Page 116
3.6 Infinite Horizon and Stationarity......Page 126
3.7 Model Types......Page 132
4 The Maximum Principle: Pure State and Mixed Inequality Constraints......Page 147
4.1 Jumps in Marginal Valuations......Page 149
4.2 The Optimal Control Problem with Pure and Mixed Constraints......Page 151
4.3 The Maximum Principle: Direct Method......Page 154
4.4 Sufficiency Conditions: Direct Method......Page 158
4.5 The Maximum Principle: Indirect Method......Page 159
4.6 Current-Value Maximum Principle:Indirect Method......Page 169
5 Applications to Finance......Page 181
5.1.1 The Model......Page 182
5.1.2 Solution by the Maximum Principle......Page 183
5.2 Optimal Financing Model......Page 186
5.2.1 The Model......Page 187
5.2.2 Application of the Maximum Principle......Page 189
5.2.3 Synthesis of Optimal Control Paths......Page 192
5.2.4 Solution for the Infinite Horizon Problem......Page 202
6 Applications to Production and Inventory......Page 212
6.1.1 The Production-Inventory Model......Page 213
6.1.2 Solution by the Maximum Principle......Page 214
6.1.3 The Infinite Horizon Solution......Page 217
6.1.4 Special Cases of Time Varying Demands......Page 218
6.1.5 Optimality of a Linear Decision Rule......Page 221
6.1.6 Analysis with a Nonnegative Production Constraint......Page 223
6.2 The Wheat Trading Model......Page 225
6.2.1 The Model......Page 226
6.2.3 Solution of a Special Case......Page 227
6.2.4 The Wheat Trading Model with No Short-Selling......Page 229
6.3 Decision Horizons and Forecast Horizons......Page 234
6.3.2 Horizons for the Wheat Trading Model with No Short-Selling and a Warehousing Constraint......Page 235
7 Applications to Marketing......Page 245
7.1.1 The Model......Page 246
7.1.2 Solution by the Maximum Principle......Page 248
7.1.3 Convex Advertising Cost and Relaxed Controls......Page 252
7.2 The Vidale-Wolfe Advertising Model......Page 255
7.2.1 Optimal Control Formulation for the Vidale-Wolfe Model......Page 256
7.2.2 Solution Using Green\'s Theorem When Q Is Large......Page 257
7.2.3 Solution When Q Is Small......Page 265
7.2.4 Solution When T Is Infinite......Page 267
8.1 Nonlinear Programming Problems......Page 278
8.1.1 Lagrange Multipliers......Page 279
8.1.2 Equality and Inequality Constraints......Page 281
8.1.3 Constraint Qualification......Page 286
8.1.4 Theorems from Nonlinear Programming......Page 287
8.2.1 A Discrete-Time Optimal Control Problem......Page 288
8.2.2 A Discrete Maximum Principle......Page 289
8.2.3 Examples......Page 291
8.3 A General Discrete Maximum Principle......Page 295
9 Maintenance and Replacement......Page 301
9.1.1 The Model......Page 302
9.1.2 Solution by the Maximum Principle......Page 303
9.1.3 A Numerical Example......Page 305
9.1.4 An Extension......Page 307
9.2 Maintenance and Replacement for a Machine Subject to Failure......Page 308
9.2.1 The Model......Page 309
9.2.2 Optimal Policy......Page 311
9.2.3 Determination of the Sale Date......Page 314
9.3.1 The Model......Page 315
9.3.2 Solution by the Discrete Maximum Principle......Page 317
9.3.4 Incorporation into the Wagner-Whitin Framework for a Complete Solution......Page 319
9.3.5 A Numerical Example......Page 320
10 Applications to Natural Resources......Page 328
10.1.1 The Dynamics of Fishery Models......Page 329
10.1.2 The Sole Owner Model......Page 330
10.1.3 Solution by Green\'s Theorem......Page 331
10.2.1 The Forestry Model......Page 334
10.2.2 Determination of Optimal Thinning......Page 335
10.2.3 A Chain of Forests Model......Page 338
10.3.1 Formulation of the Model......Page 341
10.3.2 Solution by the Maximum Principle......Page 344
11.1 Models of Optimal Economic Growth......Page 351
11.1.2 Solution by the Maximum Principle......Page 352
11.1.3 Introduction of a Growing Labor Force......Page 354
11.1.4 Solution by the Maximum Principle......Page 355
11.2.1 Formulation of the Model......Page 359
11.2.2 Solution by Green\'s Theorem......Page 360
11.3 A Pollution Control Model......Page 362
11.3.1 Model Formulation......Page 363
11.3.2 Solution by the Maximum Principle......Page 364
11.3.3 Phase Diagram Analysis......Page 365
11.4.1 Model Formulation......Page 368
11.4.2 The Implementation Problem......Page 369
11.4.3 The Optimization Problem......Page 370
11.5 Miscellaneous Applications......Page 376
12 Stochastic Optimal Control......Page 380
12.1 Stochastic Optimal Control......Page 381
12.2 A Stochastic Production Inventory Model......Page 385
12.2.1 Solution for the Production Planning Problem......Page 387
12.3 The Sethi Advertising Model......Page 390
12.4 An Optimal Consumption-Investment Problem......Page 392
12.5 Concluding Remarks......Page 398
13 Differential Games......Page 400
13.1 Two-Person Zero-Sum Differential Games......Page 401
13.2 Nash Differential Games......Page 402
13.2.2 Feedback Nash Solution......Page 403
13.2.3 An Application to Common-Property Fishery Resources......Page 404
13.3 A Feedback Nash Stochastic Differential Game in Advertising......Page 407
13.4 A Feedback Stackelberg Stochastic Differential Game of Cooperative Advertising......Page 410
A.1 First-Order Linear Equations......Page 423
A.3 System of First-Order Linear Equations......Page 424
A.4 Solution of Linear Two-Point Boundary Value Problems......Page 427
A.5 Solutions of Finite Difference Equations......Page 428
A.5.1 Changing Polynomials in Powers of k into Factorial Powers of k......Page 429
A.5.2 Changing Factorial Powers of k into OrdinaryPowers of k......Page 430
B Calculus of Variations and Optimal Control Theory......Page 432
B.1 The Simplest Variational Problem......Page 433
B.2 The Euler-Lagrange Equation......Page 434
B.4 The Brachistochrone Problem......Page 437
B.5 The Weierstrass-Erdmann CornerConditions......Page 440
B.6 Legendre\'s Conditions: The Second Variation......Page 441
B.7 Necessary Condition for a StrongMaximum......Page 442
B.8 Relation to Optimal Control Theory......Page 443
C An Alternative Derivation of the Maximum Principle......Page 446
C.1 Needle-Shaped Variation......Page 447
C.2 Derivation of the Adjoint Equation and the Maximum Principle......Page 449
D.1 The Kalman Filter......Page 453
D.2 Wiener Process and Stochastic Calculus......Page 456
D.3 The Kalman-Bucy Filter......Page 459
D.4 Linear-Quadratic Problems......Page 460
D.4.1 Certainty Equivalence or Separation Principle......Page 463
D.5 Second-Order Variations......Page 464
D.6 Singular Control......Page 466
D.7 Global Saddle Point Theorem......Page 468
D.8 The Sethi-Skiba Points......Page 470
D.9 Distributed Parameter Systems......Page 472
E Answers to Selected Exercises......Page 477
Bibliography......Page 485
Index......Page 559