Calculus of Variations and Optimal Control Theory: A Concise Introduction by Daniel Liberzon (PDF)

Description

This textbook offers a concise yet rigorous introduction to calculus of variations and optimal control theory, and is a self-contained resource for graduate students in engineering, applied mathematics, and related subjects. Designed specifically for a one-semester course, the book begins with calculus of variations, preparing the ground for optimal control. It then gives a complete proof of the maximum principle and covers key topics such as the Hamilton-Jacobi-Bellman theory of dynamic programming and linear-quadratic optimal control. Calculus of Variations and Optimal Control Theory also traces the historical development of the subject and features numerous exercises, notes and references at the end of each chapter, and suggestions for further study. Offers a concise yet rigorous introduction Requires limited background in control theory or advanced mathematics Provides a complete proof of the maximum principle Uses consistent notation in the exposition of classical and modern topics Traces the historical development of the subject Solutions manual (available only to teachers) Leading universities that have adopted this book include: University of Illinois at Urbana-Champaign ECE 553: Optimum Control Systems Georgia Institute of Technology ECE 6553: Optimal Control and Optimization University of Pennsylvania ESE 680: Optimal Control Theory University of Notre Dame EE 60565: Optimal Control

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book gives a good explanation of the 3 major approaches to Optimal Control Theory: Classical, HJB, and the Maximum Principle. This is the reason I bought it. In addition, the book itself is attractively packaged with a portrait of LaGrange himself (I assume) sitting around a table with a modern day student. LaGrange coined the expression “Calculus of Variations” and his approach is the classical one that most students first meet. The rest of the book is devoted to generalizations of and alternative approaches to the classical field. The problems are very challenging but rewarding in the long run.I recommend this book to anyone who’s interested in the field for pleasure or work. I wish that I had had this book in working some Optimal Control problems in my work as an aeronautical & astronautical engineer. Frank Lewis’ Optimal Control book is also a good source and supplement to this book (or vice versa).

⭐This book achieves the goal of being mathematically very concise and at the same time being very accessible. It is suitable for self study as well as a textbook. The book is meticulously written, the author has a great sense of humour, and has no errors that I have found. Its relative brevity is a big plus, since the author obviously made an effort to capture the essence of the subject matter.

⭐Idea of the book is better than the execution. I personally prefer books that state results, then prove them (and ideally provide motivation and context). Here, there are a lot of half proofs that are intentionally incomplete, making the development of the subject continuous, but the proofs less clear.

⭐Out of four optimal control textbooks I found this the most straightforward to follow.

⭐Very good read. I am halfway through a semester course based on this book. The book is mathematically rigorous without being longwinded. It includes much of the historical context in which much of the mathematics was discovered, making it very interesting and accessible.

⭐Liberzon’s book gives a well laid out introduction to the background material: covering all the bases without being overly technical. It also provides an excellent guide to Pontryagin’s theorem, the basis of modern control theory. A very good text!

⭐Perfect!!!

⭐This is a very good book. Although it is written with formal math in kind, the style and presentation is such that it can be of value to scientists and engineers. I think that it is a much better book than

⭐which targets the same topic and has the same goals. An additional advantage is, and I will praise the author for this, that a pre-publication version (in pdf format) has been released with a quick note from the author. This free draft can be downloaded for free. (I will not attempt to provide a URL as Amazon eliminates them. Do a quick search on the WWW and hopefully you will find it.)I must then explain my three-star rating. The author ends the preface (both in the free draft and the published version) with the following paragraph: “I decided not to eliminate all errors from the book, and instead left several of them on purpose in undisclosed locations as a way to provide additional educational experience. To report success stories of correcting errors, please contact me at my current email address (which is easy to find on the web).” Although, I fully understand this paragraph for the free draft, it kind irritates and upsets me for the published version. And below I explain the reason.I thought that every author cares to correct all typos in anything he/she writes. Certainly, there is no error-free document, but all remaining errors are usually whatever the hard work of the author, the testing audience and finally the cautious reading of proofreaders and editors did not catch before publication. But to discover typos and decide not to eliminate them, then this is a serious disservice to the readers. Imagine the following scenarios for people who learn the topic (and hence rely completely on the book) but they are unable to catch the errors: What if the errors are in statements of theorems (resulting in learning the theorem incorrectly)? What if they learn a proof that contains an incorrect argument which nullifies it? What if an error is in an end-of-charter problem making its solution impossible (thus wasting numerous hours from a serious student’s time)? I must admit that I have not read the entire book closely and hence I cannot provide a list as to what the errors are. However, for the above scenarios and many other reasons, the author should have chosen to correct the known errors (especially when he has done some other corrections and small editing changes as he reveals in his brief note in the free draft). If allowing errors in books was making reading a better education experience, shouldn’t all books have errors in undisclosed locations on purpose? And wouldn’t `the more errors, the better experience’ be a fact? Unfortunately for the author, this is not the case. Imagine the mess to be created if all books had errors on purpose. No one would be able to know what is right and what is wrong. No source would be reliable, no author to be trusted. We get a better education experience when everything we read is valuable. And it is valuable, when it its correct and to the point. Therefore, I hope that the author will consider to eliminate the above-mentioned paragraph from the preface in a second edition and, along these lines, correct all errors known to him.

⭐Very high quality advanced book on this subject, which is suitable for self reading also. Beautifully written with a good Mathematical rigour.

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