Optimal control theory is a branch of applied mathematics that deals with finding a control law for a dynamical system over a period of time such that an objective function is optimized. Pages in category calculus of variations and optimal control. This book is an introduction to both the classical theory of the calculus of variations and the more modern developments of optimal control theory from the perspective of an applied mathematician. It also includes an introduction to the classical calculus of variations. The subject cv is a pretty old subject 250 years or so and it is motivated. This textbook offers a concise yet rigorous introduction to calculus of variations and optimal control theory, and is a selfcontained resource for graduate students in engineering, applied mathematics, and related subjects. The reader interested in an introduction to the classical and. Classical mechanics with calculus of variations and optimal. Nandakumarany 1 introduction optimal control problems in some sense can be viewed as dynamic optimization and hence it is considered as a generalization of the classical calculus of variations cv. In this introduction to the calculus of variations and optimal control, we will encounter various applications while carefully developing much of the relevant mathematical theory. The course will introduce both the classical theory of the calculus of variations and the more modern developments of optimal control theory, and is potentially of interest not only to mathematics majors but also to students in the life, management, natural and social sciences.
Its applications now embrace a variety of new disciplines, including economics and production planning. A primer on the calculus of variations and optimal control. Jan 01, 2009 a primer on the calculus of variations and optimal control theory volume 50 of student mathematical library. Primer on optimal control theory provides a rigorous introduction to analyzing these processes and finding the best modes of control and operation for them. General lagrangian constraints 404 a control sets described by lagrangian inequalities 405. 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. Starting with calculus of variations and optimal control.
Pedregal 81, giustis more regularity theoryfocused introduction to the calculus of variations 44, as well as lecture notes on several related courses by j. While preparingthe lectures, i have accumulated an entire shelf of textbooks on calculus of variations and optimal control systems. It then gives a complete proof of the maximum principle and covers key topics such as the hamiltonjacobibellman theory of dynamic programming and. The calculus of variations 4 optimal control 9 2 optimization in u functions of one variable critical points, endpoints, and points of discontinuity 16 functions of several variables 18 minimization with constraints 22 a geometrical interpretation 25 distinguishing maxima from minima 28 3 the calculus of variations 33.
Daniel liberzoncalculus of variations and optimal control theory. The necessary background is mainly a strong understanding of multivariable calculus and ordinary differential equations. Lectures on the calculus of variations and optimal control theory. Mike mestertongibbons the calculus of variations is used to find functions that optimize quantities expressed in terms of integrals.
The history of the calculus of variations is tightly interwoven with the history of mathematics, 9. Optimal control theory seeks to find functions that minimize cost integrals for systems described by differential equations. A primer on the calculus of variations and optimal control theory volume 50 of student mathematical library. Everyday low prices and free delivery on eligible orders. What are some good books on calculus of variations. Applications described in this book include cancer chemotherapy, navigational control, and renewable resource. The whole topic has been extensively studied since the beginning of the twentieth century and has been recently revived by its close links with optimal control theory. Sufficient conditions for infinitehorizon calculus of variations problems. Request pdf primer on optimal control theory the performance of a. Primer on optimal control theory request pdf researchgate. A wonderful book is variational principles of mechanics by cornelius lanczos. The eulerlagrange equation associated to the functional j is. For example, the dynamical system might be a spacecraft with controls corresponding to rocket thrusters, and the objective might be to reach the. The discussion in part i is restricted to the simplest problem of the calculus of variations.
This textbook offers a concise yet rigorous introduction to calculus of variations and optimal control theory, and is a selfcontained resource for graduate students in engineering, applied. Lecture notes in calculus of variations and optimal control msc in systems and control dr george halikias eeie, school of engineering and mathematical sciences, city university 4 march 2007. Lekczii po variaczionnomu ishisleniyu i teorii optimalnogo upravleniia, leningrad we have thousands of titles and often several copies of each title may be available. Hestenes, magnus rudolph, 1906calculus of variations and optimal control theory. It is mostly about mechanics, not the calculus of variations specifically. Introduction to the mathematical theory of control. The words control theory are, of course, of recent origin, but the subject itself is much older, since it contains the classical. Welcome,you are looking at books for reading, the lectures on the calculus of variations and optimal control theory, you will able to read or download in pdf or epub books and notice some of author may have lock the live reading for some of country. An introduction to mathematical optimal control theory version 0.
Some can be solved directly by elementary arguments, others cannot. Familiarity with linear algebra and real analysis are assumed. It then gives a complete proof of the maximum principle and covers key topics such as the hamiltonjacobibellman theory of dynamic programming and linearquadratic optimal control. Optimal control reports on new theoretical and practical advances essential for analysing and synthesizing optimal controls of dynamical systems governed by partial and ordinary differential equations. Calculus of variations and optimal control theory springerlink. This pamphlet on calculus of variations and optimal control theory contains the most important results in the subject, treated largely in order of urgency. Geared toward upperlevel undergraduates, this text introduces three aspects of optimal control theory. The main body of chapter 2 consists of well known results concerning necessary or su. He also seems to enjoy himself more, considering meaty examples drawn from applications.
Sussmann cover illustration by polina bensira 2009. Mar 07, 2014 this is an intuitively motivated presentation of many topics in classical mechanics and related areas of control theory and calculus of variations. A solutions manual is available upon request for instructors. Optimal control calculus of variations, optimal control. All topics throughout the book are treated with zero tolerance for unrevealing definitions and for proofs which leave the reader in the dark. Calculus of variations and optimal control theory a concise. The present work provides a fresh approach to the calculus of variations in the presence of nonholonomic constraints. Lectures on the calculus of variations and optimal control. To be fair, when the book turns to control theory, mestertongibbons cuts himself some slack, and the book livens up a bit. After an expository account of the nature of the classical lagrange problem and a modern optimal control problem, a method is outlined which permits the transformation of a large class of optimal control problems with a compact control. Functional analysis, calculus of variations and optimal control is intended to support several different courses at the firstyear or secondyear graduate level, on functional analysis, on the calculus of variations and optimal control, or on some combination. Lectures on calculus of variations and theory of optimal control \iang l. Perhaps the book should have started with control theory, history and logical development notwithstanding.
It is desirable, although not mandatory, that the reader has also had a. Calculus of variations and optimal control august, 2014 the course material will be presented by the students in the form of lectures and discussions at the following 11 sessions, covering material from. References kamien and schwartz 1991, leeonard and long 1992, beavis and dobbs 1990, intriligator 1971, and syds. While preparingthe lectures, i have accumulated an entire shelf of textbooks on. This book is intended to present an introductory treatment of the calculus of variations in part i and of optimal control theory in part ii. Starting with calculus of variations and optimal control theory. Sussmann november 1, 2000 here is a list of examples of calculus of variations andor optimal control problems. Lectures on calculus of variations and theory of optimal control\iang l. Requires limited background in control theory or advanced mathematics. This book grew out of my lecture notes for a graduate course on optimal control theory which i taught at the university of illinois at urbanachampaign during the period from 2005 to 2010. The book can be used as a text for an advanced undergraduate or beginning graduate course, or for selfstudy. Buy a primer on the calculus of variations and optimal control theory student mathematical library by mike mestertongibbons isbn.
Calculus of variations and optimal control theory sciencedirect. Calculus of variations and optimal control itc books. It has numerous applications in both science and engineering. N2 this textbook offers a concise yet rigorous introduction to calculus of variations and optimal control theory, and is a selfcontained resource for graduate students. Please feel free to request a detailed description. Calculus of variations and optimal control theory book. Functional analysis, calculus of variations and optimal. Calculus of variations and optimal control theory a concise introduction, daniel liberzon, jan 10, 2012, mathematics, 235 pages. R calculus of variations and optimal control theory. Numerous problems, which introduce additional topics and illustrate basic concepts, appear throughout the text. Controllability, linear time optimal control, pontrjagins maximum principle for nonlinear problems, feedback control and matrix riccati equation, numerical techniques suggested reading. An introduction to mathematical optimal control theory. A primer on the calculus of variations and optimal control theory. This textbook offers a concise yet rigorous introduction to calculus of variations and optimal control theory, and is a selfcontained resource for graduate students.
Dec 19, 2011 calculus of variations and optimal control theory book. Calculus of variations and optimal control theory daniel liberzon. Evans department of mathematics university of california, berkeley chapter 1. This textbook offers a concise yet rigorous introduction to calculus of variations and optimal control theory, and is a selfcontained resource for graduate students in. It focuses on understanding concepts and how to apply them.
For this reason, it has been organized with customization in mind. Calculus variations optimal control theory abebooks. There may be more to it, but that is the main point. Therefore it need a free signup process to obtain the book. Primer on optimal control theory society for industrial. Variational calculus and optimal control springerlink. Optimal control theory seeks to find functions that minimize cost integrals for. Linear timeoptimal problems 397 problem statement 398 a free space docking problem 401 11. New necessary and sufficient conditions for optimality are given. Calculus of variation is a special case of optimal control theory in a particular sense consider, didos isoperimetric problem colloquially said to be the oldest calculus of variation problem which can be viewed as an optimal control problem, in the sense that what you get to control is the shape of the curve, and your objective is to maximize the area.
Calculus of variations and optimal control theory by hans sagan department of mathematics north carolina state university, raleigh, north carolina abstract. Hammond autumn 20, revised 2014 university of warwick, ec9a0 maths for economists peter j. Linear time optimal problems 397 problem statement 398 a free space docking problem 401 11. Constrained calculus of variations and geometric optimal. Calculus of variations and optimal control theory a. Calculus of variations, infinitehorizon problems, optimal growth theory. Pdf calculus of variations and optimal control theory.
9 65 277 1250 1537 1297 1017 1523 641 6 1498 1597 1466 768 544 1412 957 519 536 402 1192 998 255 793 108 1664 1574 1121 90 343 1012 224 1032 95 378 396 189 368