A rigorous introduction to optimal control theory, with an emphasis on applications in economics. Still i think luenberger opt by vs methods is always worth a look. Optimal control theory with economic applications volume. Thomas webers book provides a highly accessible exposition of optimal control theory and games theory, as well as of the techniques of nonlinear analysis on which they are based. Van longs optimal control theory and static optimization in economics in terms of building intuitions. This textbook is designed to make the difficult subject of optimal control theory easily accessible to economists while at the same time maintaining rigour. Optimal control methods are used to determine optimal ways to control a dynamic system. Ok covers calculus of variations not optimal control. The theoretical work in this field serves as a foundation for the book, which the authors have applied to business management problems developed from their research and classroom instruction. Optimal control theory with economic applications, volume 24 1st. Technically rigorous and largely selfcontained, it provides an introduction to the use of optimal control theory for deterministic continuoustime systems in economics. 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.
The more definite concept of a largescale system isimplicit in these applications, but is particularly evident infields such as. While preparingthe lectures, i have accumulated an entire shelf of textbooks on. Some of them focus on rigorous presentation of the theory either in the discrete or in the continuous context, others on applications in various disciplines. Jul 31, 2000 sethi and thompson have provided management science and economics communities with a thoroughly revised edition of their classic text on optimal control theory.
An introduction to mathematical optimal control theory. Thomas a weber this book bridges optimal control theory and economics, discussing ordinary differential equations, optimal control, game theory, and mechanism design in one volume. Optimal control theory with applications in economics on jstor. The calculus of variations and optimal control in economics and management advanced textbooks in economics morton i. It has been applied to a great many areas of economics and management science, such as optimal growth. Inspired by, but distinct from, the hamiltonian of classical mechanics, the hamiltonian of optimal control theory was developed by lev pontryagin as. Use features like bookmarks, note taking and highlighting while reading optimal control theory and static optimization in. More formally, an optimal control problem means endogenously controlling a parameter in a mathematical model to produce an optimal output, using some optimization. There is a number of books of various nature on optimal control theory. Optimal control theory applications to management science and. The book exploits optimal control theory to the functional areas of management science including finance, production and marketing and to economics of growth and of natural resources. It can be understood as an instantaneous increment of the lagrangian expression of the problem that is to be optimized over a certain time horizon. Optimal control theory with applications to resource and. Introductory optimization dynamics optimal control with.
Op are you planning to build a time machine to revolutionize economics in the 1970s. An excellent financial research tool, this celebrated classic focuses on the methods of solving continuous time problems. This book bridges optimal control theory and economics, discussing ordinary differential equations, optimal control, game theory, and mechanism design in one volume. In addition, this new edition features materials on stochastic nash and stackelberg differential games and an adverse selection model in the principalagent. For example, the dynamical system might be a spacecraft with controls corresponding to rocket thrusters, and the objective might be to reach the. This chapter discusses the global asymptotic stability of optimal control systems with applications to the theory of economic growth. The calculus of variations and optimal control in economics and management, morton s. Optimal control theory with economic applications ebook. An introduction to the theory and its applications by peter falb and michael athans, also published by dover. Chapter 6 considers production and inventory problems. A wide constituency of readers, from economics to applied mathematics, engineering and management science, will benefit from its clear exposition, motivational discussion and insights, and a wealth of examples in economics. Economic intuitions are emphasized, and examples and problem sets covering a.
Optimal control theory is a technique being used increasingly by academic economists to study problems involving optimal decisions in a multiperiod framework. Consider the problem of a spacecraft attempting to make a soft landing on the moon using a minimum amount of fuel. Optimal control is currently being used to push the frontiers of deep learning. This book bridges optimal control theory and economics, discussing ordinary differential equations, optimal control, game theory, and.
Optimal control theory, algorithms, and applications. If youre looking for a free download links of optimal control theory and static optimization in economics pdf, epub, docx and torrent then this site is not for you. This book is designed to make the difficult subject of optimal control theory easily accessible to economists while at. A new edition of the classic text on optimal control theory as a superb introductory text and an indispensable reference, this new edition of optimal control will serve the needs of both the professional engineer and the advanced student in mechanical, electrical, and aerospace engineering. The note should therefore be read together with articles or books that give more discussion of the economics of the problems considered. Use features like bookmarks, note taking and highlighting while reading optimal control theory and static optimization in economics. I should admit, however, that having a limited background in mathematics, i do not benefit from this book as much as a.
Optimal control theory with economic applications volume 24 advanced textbooks in economics volume 24 3rd edition. To sum up, it is a great book on introduction of optimization method in macroeconomics. This task presents us with these mathematical issues. The theory of ordinary differential equations is the. The qualitative study of optimal economic growth has attracted the attention of economic theorists for a few years.
In our book we deal exclusively with discrete optimal control problems. It has numerous applications in both science and engineering. Luenberger is more theoretical than sontag i think. He is, among others, coauthor of the popular textbook sethi and thompson.
Technically rigorous and largely selfcontained, it provides an introduction to the use of optimal control theory for deterministic. Purchase optimal control theory with economic applications, volume 24 1st edition. The methods mentioned in the book is probably basic and important for every econ student. Optimal control theory with applications in economics. Optimal control and dynamic games has been edited to honor the outstanding contributions of professor suresh sethi in the fields of applied optimal control. Optimal control theory with economic applications, volume. Although most useful part is about optimal control, getting a sense of calculus of variation will help you fully master the new optimization method. Optimal control paul schrimpf october 3, 2019 university of british columbia economics 526 cba1 1. This book bridges optimal control theory and economics, discussing ordinary differential equations, optimal control, game theory, and mechanism design in one. Optimal control theory and static optimization in economics kindle edition by leonard, daniel, long, ngo van. Download optimal control theory and static optimization in. Sethi and thompson have provided management science and economics communities with a thoroughly revised edition of their classic text on optimal control theory. The next example is from chapter 2 of the book caste. Introduction to optimal control one of the real problems that inspired and motivated the study of optimal control problems is the next and so called \moonlanding problem.
References from our text books are chapter 10 of dixit 1990, chapter 20 chiang and wainwright 2005, and chapter 12. The hamiltonian approach to dynamic economics sciencedirect. Optimal control theory and static optimization in economics. This textbook is designed to make the difficult subject of optimal control theory easily accessible to economists while at. The twopart treatment covers the calculus of variations and optimal control. In other words, we should reinvest all the output and therefore consume nothing up until time t. Also, i would recommend looking at the videos of the edx course underactuated robotics, taught by professor russ tedrake of mit.
This is a required book for my do course in economics. February 27 march 1, 1997, the conference optimal control. Optimal control techniques are being used for years in designing optimal chemotherapies in hiv 34,35 and cancer 3536373839, in optimal vaccination and treatment for epidemics 40,41. The hamiltonian is a function used to solve a problem of optimal control for a dynamical system. This book is designed to make the difficult subject of optimal control theory easily accessible to economists while at the same time maintaining rigor. The overflow blog how the pandemic changed traffic trends from 400m visitors across 172 stack. Optimal control theory with applications in economics infoscience. In the decades since its initial publication, this text has defined dynamic optimization courses taught to economics and management science students. In addition, this new edition features materials on stochastic nash and stackelberg differential games and an adverse selection model in the principalagent framework. Cambridge core econometrics and mathematical methods optimal control theory and static optimization in economics by daniel leonard. I dont know sontag but oks book covers optimal control, and better yet is webers which is shorter and includes better economic applications. Economic intuition is emphasized, examples and problem sets covering a wide range of applications in economics are provided, theorems are clearly stated and their proofs are carefully explained.
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 conference brought together researchers from universities, industry, and government laborato ries in the. Download it once and read it on your kindle device, pc, phones or tablets. Optimal control theory 6 3 the intuition behind optimal control theory since the proof, unlike the calculus of variations, is rather di cult, we will deal with the intuition behind optimal control theory instead. Browse other questions tagged referencerequest optimization bookrecommendation controltheory optimalcontrol or ask your own question.
An optimal control problem entails the identification of a feasible scheme, policy, program, strategy, or campaign, in order to achieve the optimal possible outcome of a system. Optimal control theory with applications in economics by. The concept of a system as an entity in its own right has emergedwith increasing force in the past few decades in, for example, theareas of electrical and control engineering, economics, ecology,urban structures, automaton theory, operational research andindustry. This fully revised textbook offers an introduction to optimal control theory and its diverse applications in management and economics. Agec 642 lectures in dynamic optimization optimal control and numerical dynamic programming richard t. Optimal control theory with applications in economics the mit. Its coverage encompasses all the fundamental topics as well as the major changes that have occurred in. Central to the book is its extraordinarily wide range of optimal control theory applications. The long awaited second edition of dynamic optimization is now available. The book exploits optimal control theory to the functional areas of management including finance, production and marketing and to economics of growth and of natural resources.
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