Dynamic Programming and Optimal Control: Volume I, Volume 1

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Athena Scientific, 2012 - Mathematics - 613 pages

This is the leading and most up-to-date textbook on the far-ranging algorithmic methododogy of Dynamic Programming, which can be used for optimal control, Markovian decision problems, planning and sequential decision making under uncertainty, and discrete/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 extensive treatment of the far-reaching methodology of Neuro-Dynamic Programming/Reinforcement Learning.

Among its special features, the book 1) provides a unifying framework for sequential decision making, 2) treats simultaneously deterministic and stochastic control problems popular in modern control theory and Markovian decision popular in operations research, 3) develops the theory of deterministic optimal control problems including the Pontryagin Minimum Principle, 4) introduces recent suboptimal control and simulation-based approximation techniques (neuro-dynamic programming), which allow the practical application of dynamic programming to complex problems that involve the dual curse of large dimension and lack of an accurate mathematical model, 5) provides a comprehensive treatment of infinite horizon problems in the second volume, and an introductory treatment in the first volume

The electronic version of the book includes 29 theoretical problems, with high-quality solutions, which enhance the range of coverage of the book.

 

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Contents

The Dynamic Programming Algorithm
1
Deterministic Systems and the Shortest Path Problem
67
Problems with Perfect State Information
109
Problems with Imperfect State Information
183
Introduction to Infinite Horizon Problems
231
Approximate Dynamic Programming
291
Deterministic ContinuousTime Optimal Control
425
Mathematical Review
467
On Optimization Theory
476
On Probability Theory
480
On FiniteState Markov Chains
485
Least Squares Estimation and Kalman Filtering
489
Formulating Problems of Decision Under Uncertainty
511
References
533
Index
551
Selected Theoretical Problem Solutions
1

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About the author (2012)

Dimitri P. Bertsekas undergraduate studies were in engineering at the National Technical University of Athens, Greece. He obtained his MS in electrical engineering at the George Washington University, Wash. DC in 1969, and his Ph.D. in system science in 1971 at the Massachusetts Institute of Technology.

Dr. Bertsekas has held faculty positions with the Engineering-Economic Systems Dept., Stanford University (1971-1974) and the Electrical Engineering Dept. of the University of Illinois, Urbana (1974-1979). From 1979 to 2019 he was with the Electrical Engineering and Computer Science Department of the Massachusetts Institute of Technology (M.I.T.), where he served as McAfee Professor of Engineering. In 2019, he was appointed Fulton Professor of Computational Decision Making, and a full time faculty member at the department of Computer, Information, and Decision Systems Engineering at Arizona State University (ASU), Tempe, while maintaining a research position at MIT. His research spans several fields, including optimization, control, large-scale computation, and data communication networks, and is closely tied to his teaching and book authoring activities. He has written numerous research papers, and eighteen books and research monographs, several of which are used as textbooks in MIT and ASU classes. Most recently Dr Bertsekas has been focusing on reinforcement learning, and authored a textbook in 2019, and a research monograph on its distributed and multiagent implementation aspects in 2020.

Professor Bertsekas was awarded the INFORMS 1997 Prize for Research Excellence in the Interface Between Operations Research and Computer Science for his book "Neuro-Dynamic Programming", the 2000 Greek National Award for Operations Research, the 2001 ACC John R. Ragazzini Education Award, the 2009 INFORMS Expository Writing Award, the 2014 ACC Richard E. Bellman Control Heritage Award for "contributions to the foundations of deterministic and stochastic optimization-based methods in systems and control," the 2014 Khachiyan Prize for Life-Time Accomplishments in Optimization, the SIAM/MOS 2015 George B. Dantzig Prize, and the 2022 IEEE Control Systems Award. In 2018, he was awarded, jointly with his coauthor John Tsitsiklis, the INFORMS John von Neumann Theory Prize, for the contributions of the research monographs "Parallel and Distributed Computation" and "Neuro-Dynamic Programming". In 2001, he was elected to the United States National Academy of Engineering for "pioneering contributions to fundamental research, practice and education of optimization/control theory, and especially its application to data communication networks."

Dr. Bertsekas' recent books are "Introduction to Probability: 2nd Edition" (2008), "Convex Optimization Theory" (2009), "Dynamic Programming and Optimal Control," Vol. I, (2017), and Vol. II: (2012), "Abstract Dynamic Programming" (2018), "Convex Optimization Algorithms" (2015), "Reinforcement Learning and Optimal Control" (2019), and "Rollout, Policy Iteration, and Distributed Reinforcement Learning" (2020), all published by Athena Scientific.

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