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- Product code: 15786
- ISBN: 1886529094,
ISBN13: 9781886529090,
520 pages, hardback
Published by Athena Scientific on 2000
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Description of Dynamic Programming & Optimal Control: 1 |
A substantially expanded and improved edition of the best-selling textbook by Bertsekas on dynamic programming. This is a far-ranging algorithmic methododogy for optimal control, sequential decision making under uncertainty, and combinatorial optimization. The treatment focuses on basic unifying themes, and conceptual foundations. It illustrates the versatility, power, and generality of the method with many examples and applications from engineering, operations research, and other fields. It also addresses extensively the practical application of the methodology, possibly through the use of approximations, and provides an introduction to the far-reaching methodology of neuro-dynamic programming.
The first volume is oriented towards modeling, conceptualization, and finite-horizon problems, but also includes a substantive introduction to infinite horizon problems that is suitable for classroom use.
The second volume (see book 15787) is oriented towards mathematical analysis and computation, and treats infinite horizon problems extensively. The text contains many illustrations, worked-out examples, and exercises.
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Reviews'In conclusion, this book is an excellent source of reference ... The main strengths of the book are the clarity of the exposition, the quality and variety of the examples, and its coverage of the most recent advances.'
Thomas W. Archibald, in IMA Jnl. of Mathematics Applied in Business & Industry
'Here is a tour-de-force in the field.'
David K. Smith, in Jnl. of Operational Research Society
'By its comprehensive coverage, very good material organization, readability of the exposition, included theoretical results, and its challenging examples and exercises, the reviewed book is highly recommended for a graduate course in dynamic programming or for self-study. It is a valuable reference for control theorists, mathematicians, and all those who use systems and control theory in their work. Students will for sure find the approach very readable, clear, and concise. Misprints are extremely few.'
Vasile Sima, in SIAM Review
'In this two-volume work Bertsekas caters equally effectively to theoreticians who care for proof of such concepts as the existence and the nature of optimal policies and to practitioners interested in the modeling and the quantitative and numerical solution aspects of stochastic dynamic programming.'
Michael Caramanis, in Interfaces
'The textbook by Bertsekas is excellent, both as a reference for the course and for general knowledge. It is well written, clear and helpful'
Student evaluation guide for the Dynamic Programming and Stochastic Control course at the Massachusetts Institute of Technology
| Contents of Dynamic Programming & Optimal Control: 1 |
The Dynamic Programming Algorithm
1. Introduction
2. The Basic Problem
3. The Dynamic Programming Algorithm
4. State Augmentation
5. Some Mathematical Issues
6. Notes, Sources, and Exercises
Deterministic Systems and the Shortest Path Problem
1. Finite-State Systems and Shortest Paths
2. Some Shortest Path Applications
1. Critical Path Analysis
2. Hidden Markov Models and the Viterbi Algorithm
3. Shortest Path Algorithms
1. Label Correcting Methods
2. Auction Algorithms
4. Notes, Sources, and Exercises
Deterministic Continuous-Time Optimal Control
1. Continuous-Time Optimal Control
2. The Hamilton-Jacobi-Bellman Equation
3. The Pontryagin Minimum Principle
1. An Informal Derivation Using the HJB Equation
2. A Derivation Based on Variational Ideas
3. The Minimum Principle for Discrete-Time Problems
4. Extensions of the Minimum Principle
1. Fixed Terminal State
2. Free Initial State
3. Free Terminal Time
4. Time-Varying System and Cost
5. Singular Problems
5. Notes, Sources, and Exercises
Problems with Perfect State Information
1. Linear Systems and Quadratic Cost
2. Inventory Control
3. Dynamic Portfolio Analysis
4. Optimal Stopping Problems
5. Scheduling and the Interchange Argument
6. Set-Membership Description of Uncertainty
1. Set-Membership Estimation
2. Control with Unknown-but-Bounded Disturbances
7. Notes, Sources, and Exercises
Problems with Imperfect State Information
1. Reductions to the Perfect Information Case
2. Linear Systems and Quadratic Cost
3. Minimum Variance Control of Linear Systems
4. Sufficient Statistics and Finite-State Markov Chains
5. Sequential Hypothesis Testing
6. Notes, Sources, and Exercises
Suboptimal and Adaptive Control
1. Certainty Equivalent and Adaptive Control
1. Caution, Probing, and Dual Control
2. Two-Phase Control and Identifiability
3. Certainty Equivalent Control and Identifiability
4. Self-Tuning Regulators
2. Open-Loop Feedback Control
3. Limited Lookahead Policies and Applications
1. Performance Bounds of Limited Lookahead Policies
2. Computational Issues in Limited Lookahead
3. Problem Approximation -- Enforced Decomposition
4. Heuristic Cost-to-Go Approximation
4. Rollout Algorithms
1. Discrete Deterministic Problems
2. Q-Factors Evaluated by Simulation
3. Q-Factor Approximation
5. Additional Topics in Suboptimal Control
1. Rolling Horizon Approximations
2. Discretization
3. Other Approximation Approaches
6. Notes, Sources, and Exercises
Introduction to Infinite Horizon Problems
1. An Overview
2. Stochastic Shortest Path Problems
3. Discounted Problems
4. Average Cost Problems
5. Semi-Markov Problems
6. Notes, Sources, and Exercises
Appendix A: Mathematical Review
Appendix B: On Optimization Theory
Appendix C: On Probability Theory
Appendix D: On Finite-State Markov Chains
Appendix E: Kalman Filtering
Appendix F: Modeling of Stochastic Linear Systems
Appendix G: Formulating Problems of Decision Under Uncertainty
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About Dimitri P. Bertsekas |
The author is McAfee Professor of Engineering at the Massachusetts Institute of Technology and a member of the National Academy of Engineering. He has been teaching the material included in this book in introductory graduate courses for over twenty five years.
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