Dynamic Programming and Optimal Control, Vol. 1 (Optimization and Computation Series) [Hardcover]

Dimitri P. Bertsekas (Author)

Book Description

Publication Date: November 15, 2000 | ISBN-10: 1886529094 | ISBN-13: 978-1886529090 | Edition: 2nd

This is a substantially expanded (by about 30%) and improved edition of Vol. 1 of the best-selling dynamic programming book by Bertsekas. (A relatively minor revision of Vol.\ 2 is planned for the second half of 2001.) DP is a central algorithmic method for optimal control, sequential decision making under uncertainty, and combinatorial optimization. The treatment focuses on basic unifying themes and conceptual foundations. It illustrates the power of the method with many examples and applications from engineering, operations research, and economics.

Among its special features, the book:

(a) provides a unifying framework for sequential decision making

(b) develops the theory of deterministic optimal control including the Pontryagin Minimum Principle

(c) describes neuro-dynamic programming techniques for practical application of DP to complex problems that involve the dual curse of large dimension and lack of an accurate mathematical model

(d) provides a comprehensive treatment of infinite horizon problems in the second volume, and an introductory treatment in the first volume

(e) contains many exercises, with solutions of the most theoretical ones posted on the book's www page

Highlights of the revision: (a) Much new material on suboptimal control, including neuro-dynamic programming and rollout algorithms, and their applications in combinatorial optimization and stochastic optimal control. (b) A section on estimation and control of systems with a non-probabilistic (set membership) description of uncertainty. (c) A section on infinite horizon continuous-time (semi-Markov) decision problems. (d) A new appendix dealing with the minimax and expected utility approaches for formulating decision problems under uncertainty.

Editorial Reviews

Review

"... this book is an excellent source of reference..." -- From

"Here is a tour-de-force in its field." -- D. Smith, Operational Research Society

About the Author

Dimitri Bertsekas is Professor of Electrical Engineering and Computer Science at the Massachusetts Institute of Technology. He consults regularly with private industry and has held editorial positions in several journals. He has been elected Fellow of the IEEE. He has researched a broad variety of subjects from optimization theory, control theory, parallel and distributed computation, systems analysis, and data communication networks. He has written numerous papers in each of these areas, and he has authored or coauthored eleven textbooks.

Product Details

• Hardcover: 530 pages
• Publisher: Athena Scientific; 2nd edition (November 15, 2000)
• Language: English
• ISBN-10: 1886529094
• ISBN-13: 978-1886529090
• Product Dimensions: 9.3 x 6.3 x 1.2 inches
• Shipping Weight: 1.8 pounds
• Average Customer Review: 3.7 out of 5 stars  See all reviews (3 customer reviews)
• Amazon Best Sellers Rank: #2,120,544 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

18 of 18 people found the following review helpful:

5.0 out of 5 stars Best book I've used so far., April 19, 2000

By 

Samuel Albert (Saint Paul, MN) - See all my reviews

This review is from: Dynamic Programming and Optimal Control (Volumes 1 and 2) (Hardcover)

This book does a very good job presenting both deterministic and stochastic optimal control. The author does a particularly good job in presenting the derivation of the Bellman equation and its relation to variational formulations for deterministic optimal control. There are also many very good problems with which the reader can test her understanding, and the author has made many solutions available on his web page. Problems range from testing theoretical understanding to determinig optimal policies for various control problems. There are even some exercises which ask the reader to develop parallel codes to solve some problems, so I think there is something in this book for everybody. Richard Bellman once said that there is considerably more to optimal control than just locating the eigenvalues of some matrix in the complex plane. I believe that Bertsekas has remained faithful to Bellman's view with the broad range of problems which he attacks through dynamic programming. I am currently doing a PhD thesis in mathematics studying Bellman equations, and I cannot think of a better source for intuition about control problems than Bertsekas' book. He even does a nice job in pointing out where he has omitted technicalities in the mathematical treatment for those who wish a very rigorous approach to control. If there is a better book out there, I am not aware of it.

4 of 6 people found the following review helpful:

3.0 out of 5 stars Understated and overstated all at once, October 10, 2009

By 

Gabriel Kron - See all my reviews

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This review is from: Dynamic Programming & Optimal Control, Vol. I (Hardcover)

After having been exposed to (and purchased) a number of books by Dr. Bertsekas on an eclectic array of topics, I have little doubt about his superb acumen and mastery of many, many subject areas involving applied mathematics. This book is no exception. Further, the legibility of Bertsekas' books score much higher the other two members of the GMTM (the Greek Math Triad of MIT), namely Bertsimas and Tsitsiklis, whose writings are highly esoteric in the purest form of the Archimedian tradition.

However, despite applaudable efforts to make the book more accessible to those on a lower IQ scale than the top-shelf MIT doctoral students, Bertsekas' 2-volume set on DP & Optimal Control still falls short in two key areas: (1) Visualization; and (2) Inconsistency in flow.

Being a product of the multi-media era, I and many of my fellow students are highly-dependent on visualization tools. In my opinion, what is NOT conveyed through lines and lines of cryptic (and author-specific) symbolism and mathematical formulation CAN be effectively conveyed through the strategic (and reasonably-ample) use of graphs and diagrams. Once the reader has a general idea of the gist of the concepts, then the specifics can be stated using precise mathematical language. But until then, the formulations are subject to open and erroneous interpretation (much the same way that few students are able to decipher the true essence of Symphony No. 40 by merely staring at the musical notes on sheets of paper). A picture is worth a thousand Greek symbols.

Inconsistency in flow refers to the fact that certain basic concepts are overstated in the book, while some of the more critical concepts (particularly those involving not-so-obvious algebraic steps in the proofs) are deemed "trivial" by the author, and apparently skipped for the sake of keeping the book to a manageable size. My suggestion is to err on the side of over-inclusion by keeping the proofs to a minimal in the actual text, but making the proofs (with all "trivial" elaborations) available online through the publisher's website (or via an included CD-ROM).

The aforesaid aside, the book is one of the best efforts in providing a comprehensive and modern analysis of DP/MDP, and its later editions do have the potential to claim 4.5-5 stars. In the interim, I recommend Powell's Approximate DP book as a less painful way of learning what I personally consider to be one of the most important topics in combinatorial optimization.

2 of 8 people found the following review helpful:

3.0 out of 5 stars not what i expected, June 4, 2008

By 

Ali (Boston, MA) - See all my reviews

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This review is from: Dynamic Programming & Optimal Control, Vol. I (Hardcover)

This book has so many unnecessary material in it. This makes you tired if you want to read it as your course book. I think Bertsekas, is more busy to write as many as book he can instead of making them readable.