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A Primer on Pontryagin's Principle in Optimal Control: Second Edition, by I. Michael Ross
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EDITORIAL REVIEW:
This book provides a guided tour in introducing optimal control theory from a practitioner’s point of view. As in the first edition, Ross takes the contrarian view that it is not necessary to prove Pontryagin’s Principle before using it. Using the same philosophy, the second edition expands the ideas over four chapters:
- In Chapter 1, basic principles related to problem formulation via a structured approach are introduced:
- What is a state variable?
- What is a control variable?
- What is state space? And so on.
- In Chapter 2, Pontryagin’s Principle is introduced using intuitive ideas from everyday life: Like the process of “measuring” a sandwich and how it relates to costates. A vast number of illustrations are used to explain the concepts without going into the minutia of obscure mathematics. Mnemonics are introduced to help a beginner remember the collection of conditions that constitute Pontryagin’s Principle.
- In Chapter 3, several examples are worked out in detail to illustrate a step-by-step process in applying Pontryagin’s Principle. Included in this example is Kalman’s linear-quadratic optimal control problem.
- In Chapter 4, a large number of problems from applied mathematics to management science are solved to illustrate how Pontryagin’s Principle is used across the disciplines. Included in this chapter are test problems and solutions.
- Sales Rank: #1334211 in Books
- Published on: 2015-03-03
- Original language: English
- Number of items: 1
- Dimensions: 9.21" h x .84" w x 6.14" l, 1.14 pounds
- Binding: Paperback
- 370 pages
About the Author
I. Michael Ross is a Professor and Program Director of Control and Optimization at the Naval Postgraduate School in Monterey, California. A Fellow of the American Astronautical Society, he received the 2010 AIAA Mechanics and Control of Flight Award for advancing pseudospectral optimal control theory and its flight implementations. His research has been featured in "How Stuff Works", SIAM News, IEEE Control Systems Magazine, IEEE Spectrum, Space Daily, and other news outlets. He authored DIDO, the world’s first general-purpose object-oriented software for optimal control. The software is used extensively across various industries to solve practical optimal control problems in astrodynamics, chemotherapy, climate control, data processing, launch vehicle design, missile guidance, quantum control, unmanned systems and much more. Ross has served on several AAS, AIAA, and NASA Technical Committees.
Most helpful customer reviews
0 of 0 people found the following review helpful.
An engineering course on how to solve problems with optimal control using the Pontryagin's principle and the Dido software
By Litsios James
This book is passionate introduction course to optimal control based on Pontryagin's principle.
The preface forewarns us, the author says something like "I show first, then explain after". And show he does! In fact, I believe the book deserves five stars for the showing. Prof. Ross takes a four front approach to educate us: lots of drawings and figures, a good amount math, a good amount of "simulation code" (for the Dido program), and a good amount of text. Anybody who has tried to write educational material knows that getting such a multi-view approach right is not easy. And here I need to say that that the book could do with a re-edit to bring everything together better. And therefore my "only" four start grading. Nevertheless, the content is good, especially when you take it as an engineering textbook and not a math book. This is book about understanding the principals and a tool, the difficulties and the solutions, and with such a focus it does very well. Also in a re-edit I would take out the overly self praise about the Dido program: let the student's learn if the tool is good!
0 of 1 people found the following review helpful.
Optimal control made easy
By ksskstar
This book is an updated version of Ross’ first book. The second edition still has the same four chapters as the first, but each chapter is expanded with lots of details and figures. Ross’ style is easygoing and humorous. For example, what is a state variable? Any variable with a dot! This is the simplest explanation I’ve ever seen. He demystifies state-space representation, Lagrange multipliers, numerical methods etc. and makes you want to learn and read more. He also provides historical accounts that I found quite fascinating. The advanced topics are marked with dangerous bends. If you are a student like me, I say skip all these sections. Perhaps someone with a more advanced background can comment on his advanced sections.
He begins chapter 2 with his famous line, “You want proof? You can’t handle the proof!” I’m ok with this because I don’t understand the “real proof” anyway. But I must say that I understand Pontryagin’s Principle better now because Ross has a new take on costates. I didn’t know I was using costates in my daily life when I was counting calories in my sandwich! Trust me, this is a real example in this book!
The book contains lots of example problems and solutions. I followed the worked out examples but had difficulty with some of the study problems. There are many other problems in this book with solutions, which are quite good, but he doesn’t explain how he got them. One new feature of the second edition is that there are a lot of example problems with DIDO solutions. A few problems have solutions from other MATLAB solvers too. I tried solving a couple of these problems and didn’t quite get them exactly the way he has it in his book, so I don’t know what I’m doing wrong.
If you want a book with “theorems and proofs”, this book is NOT for you. If you simply want to understand optimal control, then there is no other book like this one. If you already understand optimal control but want a quick go-to guide, you do not need to buy this book; just download the “Pontryagin’s Principle” chapter for free from the Elissar Global website. There are a few obvious typos here and there but it didn’t bother me too much.
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