Book Description
Geared toward advanced undergraduates and graduate engineering students, this text introduces the theory and applications of optimal control. It serves as a bridge to the technical literature, enabling students to evaluate the implications of theoretical control work, and to judge the merits of papers on the subject. 1963 edition.
Book Description
This book gives an introduction to the basic theory of stochastic calculus and its applications. Examples are given throughout the text, in order to motivate and illustrate the theory and show its importance for many applications in e.g. economics, biology and physics. The basic idea of the presentation is to start from some basic results (without proofs) of the easier cases and develop the theory from there, and to concentrate on the proofs of the easier case (which nevertheless are often sufficiently general for many purposes) in order to be able to reach quickly the parts of the theory which is most important for the applications. For the 6th edition the author has added further exercises and, for the first time, solutions to many of the exercises are provided.
Customer Reviews:
A very good book!.......2007-07-05
I read this book after I had read Karatzas' and Shreve's book "Stochastic Calculus..." and it is probably better to do it the other way round. The mathematical prerequisites are not high, however a good intuitive understanding of measure theory is probably necessary. The pace of the book is leasurely, the proofs are such, that pencil and paper is rarely needed, however no rigor is lost.
The book quickly moves to interesting applications of the theory, which is motivated very well.
It contains a few typographical errors, mostly in the last chapter, and mostly of a harmless nature.
With the necessary mathematical background, it seems to be an ideal introduction to this highly interesting topic of stochastic differential equations!
Excellent introduction on Stochastic Differential Equations.......2007-05-08
A well written book in Mathematics
Stochastic Differential Equations is a branch of mathematics. This book is not just for financial derivatives analysis or modeling. Oksendal first introduces the subject by raising a few stochastic problems (population growth; electric charge in RLC circuit; filtering problems, Dirichlet problems; asset management; optimal portfolio and options pricing) in the first chapter. The subsequent chapters develop notions and techniques which are able to solve wide varieties of stochastic problems (not just those mentioned in the first chapters). The arrangement is impressive in particular for readers who have no previous knowledge about the subject. The readers at least know the target for developing the techniques and would not lose the way when manipulating tons of symbols. Hints and answers to selected problems are invaluable to students for self-study.
To achieve a sound background on stochastic equations is extremely important especially in quantitative finance. It is not an easy job however. QF students may consider going through this book before seriously take Shreve's books on Stochastic Calculus for Finance.
OK intro to stochastic analysis.......2007-03-14
This is a standard work (it is the one I read when I first started looking at this sort of thing) but having taken it off the shelf recently again, I think it is overrated, for several reasons.
First, it is very notation heavy - TeX has seduced Mr. Oksendahl into all sorts of bad habits - I can very easily imagine that the earlier editions (mine is the 5th), which were written with a typewriter, are much more readable.
Second, the proofs are very formal, developed mostly in terms of classical functional analysis (square integrable real functions, geometry of real Hilbert spaces etc.). From the point of view of rigor this is fine, but from the point of view of intuition, not so much, esp. when combined with the heavyweight notation. In fact note that unless you have a decent background in functional analysis, of the sort you are more likely to pick up in a mathematics degree than a finance degree, then you are going to get precisely nowhere with this book.
I don't want to be too negative, and there is lots of good stuff here - just to warn that Oksendahl is not (as one might think) a royal road to the theory of SDEs (depressingly, it may be that Oksendahl is, nevertheless, the best of the bunch out there - it is certainly, all criticism not-withstanding, more accessible than Karatzas and Shreve).
Very good book - would not mind more on finance.......2007-02-08
Very good book. However the math prerequisite is at quite a high level. Especially the probability theory introduction could be a little less fast-paced. As my main interest was on the financial application I would not have minded a little more on that topic and a little less on e.g. filtering or stochatsic control in return.
good intro book.......2006-02-03
This is a good intro book. It brings you really fast to Ito's Formula and SDE. Somebody said that the Kolmogorov's backward eq in chapter 8 is wrong. This is false, it is just expressed in a different way than the usual form. However, with a change of time, you are all set.
Book Description
Presenting a thorough introductory exposition of optimal control theory, this work differs from the existing textbooks on the subject due to its emphasis on the economic interpretation of the mathematics and the qualitative properties of the solutions. Moreover, it is a modern exposition of optimal control theory in that it presents numerous complementary methods. It is aimed at first-year and second-year PhD students in economics, agricultural and resource economics, operations research, management science, and applied mathematics.
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Optimal Control (Systems & Control: Foundations & Applications)
Richard Vinter
Manufacturer: Birkhauser
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Partial Differential Equations (Graduate Studies in Mathematics, V. 19) GSM/19 (Graduate Studies in Mathematics)
ASIN: 0817640754 |
Book Description
Optimal control emerged as a distinct field of research only in recent decades. It provides a unified perspective of optimization problems, arising in scheduling and the control of engineering devices, that are beyond the reach of traditional analytical and computational techniques. In addition, the field has contributed significant advances to branches of applied mathematics and broad applications in process control, scheduling, robotics, resource economics, and other areas. Optimal Control brings together many of the important advances in 'nonsmooth' optimal control over the last two decades concerning necessary conditions, minimizer regularity and global optimality conditions associated with the Hamilton-Jacobi equation. The book's development and analysis is largely self-contained and incorporates numerous simplifications and unifying features for the subjects' key concepts and foundations. Features and Topics: * a comprehensive overview is provided for specialists and nonspecialists * authoritative, coherent and accessible coverage of the role of nonsmooth analysis in investigating minimizing curves for optimal control * chapter coverage of dynamic programming *explains the necessary conditions for nonconvex problems * chapter coverage of the regularity of minimizers This new book is an essential resource for an authoritative and comprehensive presentation of the foundations and application of nonsmooth optimal control. Postgraduates, researchers and professionals in systems, control, optimization and applied mathematics will find that the book is accessible, provides a rich source of insights and offers clear exposition.
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H-Infinity Optimal Control and Related Minimax Design Problems: A Dynamic Game Approach (Systems & Control: Foundations & Applications)
Tamer Basar , and
Pierre Bernhard
Manufacturer: Birkhäuser Boston
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ASIN: 0817638148 |
Book Description
One of the major concentrated activities of the past decade in control theory has been the development of the so-called 'H-infinity-optimal control theory', which addresses the issue of worst-case controller design for linear plants subject to unknown disturbances and plant uncertainties.
This second edition features a more streamlined presentation of the results included in the first edition and also contains substantial new material, reflecting new developments in the field since 1991. Among these are the nonlinear theory; connections between H-infinity-optimal control and risk sensitive stochastic control problems; H-infinity filtering for linear and nonlinear systems; and robustness considerations in the presence of regular and singular perturbations. Also included are a rather detailed description of the relationship between frequency-and time-domain approaches to robust controller design, and a complete set of results on the existence of value and characterization of optimal policies in finite- and infinite-horizon LQ differential games.
The authors believe that the theory is now at a stage where it can easily be incorporated into a second-level graduate course in a control curriculum, that would follow a basic course in linear control theory covering LQ and LQG designs.
Book Description
Sethi and Thompson have provided management science and economics communities with a thoroughly revised edition of their classic text on
Optimal Control Theory. Central to the book is its extraordinarily wide range of optimal control theory applications. Chapter 5 covers finance; Chapter 6 considers production and inventory problems; Chapter 7 covers marketing problems; Chapter 9 treats machine maintenance and replacement; Chapter 10 deals with problems of optimal consumption of natural resources (renewable or exhaustible); and Chapter 11 discusses a number of applications of control theory to economics. The book has been successfully used as a professional reference tool and as a graduate course book. Its usefulness lies in its emphasis on building applied models of realistic problems faced in a variety of business management situations.
The new edition has been completely refined with careful attention to the text and graphic material presentation. In Chapter 3, models have been added that use mixed (control and state) constraints, current value formulations, and terminal conditions. Chapter 4 now covers more advanced material on pure state constraints as they relate to mixed constraints. Each of these chapters contains new results that were not available when the first edition was published.
Another important change is the expansion of the material on stochastic optimal control theory, which has become the new Chapter 13. This new chapter provides a brief introduction to stochastic optimal control problems, and it contains formulations of simple stochastic models in production, marketing and finance, and their solutions.
Optimal control methods are used to determine optimal ways to control a dynamic system. 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.
Customer Reviews:
Technical Paper Rollup.......2005-02-08
Book is essentially a compendium of technical papers on specific economics topics subject to the application of Control Theory. The book includes a robust set of useful state equations and associated optimality problem statements, but I would have appreciated a more general discussion of the application of control theory to management science that ties all of the book's subjects together into a single, cohesive framework. The book focuses almost exclusively on the trees rather than the forest. As such, it is best suited as a supplement for graduate-level studies.
An extremely good textbook.......2003-03-27
This is a very good textbook for subjects on optimal controls with management science applications. I have adopted this as a textbook and students love it. Illustrative figures and diagrams are sufficiently provided, and materials are carefully explained.
The use of the commonly available Excel program to solve TPBVPs at the end of Chapter 2 is suitable for the ever increasing demand of "multimedia teaching". I have not seen any other optimal control textbook include such a set of Excel instructions in such a simple and elegant way.
Moreover, the authors made a set of chapter-by-chapter power point files available on the web to supplement the text book for classroom teaching.
I am giving 5 stars to this book anytime.
Book Description
This book presents a self-contained and up-to-date account of the theory of viscosity solutions for first order partial differential equations of Hamilton-Jacobi type and its interplay with Bellman's Dynamic Programming approach to optimal control and differential games, as it developed after the beginning of the eighties with the pioneering work of M. Crandall and P.L. Lions. The book begins with a long introduction where the authors present in a rather informal way the main ideas and themes of the book, beginning with the classical derivation of the Hamilton-Jacobi-Bellman equation from the Dynamic Programming Optimality Principle and the characterization of the value function as the unique viscosity solution of this equation. This is followed by a treatment of the general theory of continuous viscosity solutions and its applications to a number of problems in deterministic optimal control theory for nonlinear systems(infinite and finite horizon, minimal time, optimal stopping, impulse control, problems with state constraints, etc.)The second part of the book develops the theory of discontinuous viscosity solutions and its applications to asymptotic problems (singular perturbations, ergodic problems, etc.), to some approximation schemes for the value function and for optimal feedback controls based on Dynamic Programming. The last chapter and appendix deal, respectively, with differential games and nonlinear H-infinity control.
The book will be of interest to scientists involved in the theory of optimal control of deterministic linear and nonlinear systems. In particular it will appeal to system theorists wishing to learn about a recent mathematical theory providing a correct framework for the classical method of Dynamic Programming and mathematicians interested in new recent methods for first order nonlinear PDEs. The books historical notes provide a guide to a fairly complete bibliography including more than 500 titles. Some suggestions of how to present the material to students will make it ideal as a graduate course text as well as a self-teaching tool for practicing control mathematicians and engineers.
Product Description
Optimal Control and Dynamic Games has been edited to honor the outstanding contributions of Professor Suresh Sethi in the fields of Applied Optimal Control. Professor Sethi is internationally one of the foremost experts in this field. He is, among others, co-author of the popular textbook "Sethi and Thompson: Optimal Control Theory: Applications to Management Science and Economics". The book consists of a collection of essays by some of the best known scientists in the field, covering diverse aspects of applications of optimal control and dynamic games to problems in Finance, Management Science, Economics, and Operations Research. In doing so, it provides both a state-of-the-art overview over recent developments in the field, and a reference work covering the wide variety of contemporary questions that can be addressed with optimal control tools, and demonstrates the fruitfulness of the methodology.
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Optimal Control from Theory to Computer Programs (Solid Mechanics and Its Applications)
V. Arnautu , and
Pekka Neittaanmäki
Manufacturer: Springer
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ASIN: 1402017715 |
Book Description
The aim of this book is to present the mathematical theory and the know-how to make computer programs for the numerical approximation of Optimal Control of PDE's. The computer programs are presented in a straightforward generic language. As a consequence they are well structured, clearly explained and can be translated easily into any high level programming language. Applications and corresponding numerical tests are also given and discussed. To our knowledge, this is the first book to put together mathematics and computer programs for Optimal Control in order to bridge the gap between mathematical abstract algorithms and concrete numerical ones.
The text is addressed to students and graduates in Mathematics, Mechanics, Applied Mathematics, Numerical Software, Information Technology and Engineering. It can also be used for Master and Ph.D. programs.
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Control of Spatially Structured Random Processes and Random Fields with Applications (Nonconvex Optimization and Its Applications)
Ruslan K. Chornei ,
Hans Daduna , and
Pavel S. Knopov
Manufacturer: Springer
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ASIN: 0387304096 |
Book Description
This book is devoted to the study and optimization of spatiotemporal stochastic processes, that is, processes which develop simultaneously in space and time under random influences. These processes are seen to occur almost everywhere when studying the global behavior of complex systems, including:
- Physical and technical systems
- Population dynamics
- Neural networks
- Computer and telecommunication networks
- Complex production networks
- Flexible manufacturing systems
- Logistic networks and transportation systems
-Environmental engineering
Climate modelling and prediction
Earth surface models
Classical stochastic dynamic optimization forms the framework of the book. Taken as a whole, the project undertaken in the book is to establish optimality or near-optimality for Markovian policies in the control of spatiotemporal Markovian processes. The authors apply this general principle to different frameworks of Markovian systems and processes. Depending on the structure of the systems and the surroundings of the model classes the authors arrive at different levels of simplicity for the policy classes which encompass optimal or nearly optimal policies. A set of examples accompanies the theoretical findings, and these examples should demonstrate some important application areas for the theorems discussed.
Books:
- Physics for Scientists and Engineers with Modern Physics, Third Edition
- Physics for Scientists and Engineers with Modern Physics, Third Edition
- Physics: Principles with Applications (6th Edition)
- Probability and Computing: Randomized Algorithms and Probabilistic Analysis
- Probability, Random Variables, and Random Signal Principles
- Regression Methods in Biostatistics: Linear, Logistic, Survival, and Repeated Measures Models (Statistics for Biology and Health)
- Requirements Analysis: From Business Views to Architecture
- Rules of Thumb for Chemical Engineers
- Schaum's Mathematical Handbook of Formulas and Tables
- Schaum's Outline of Continuum Mechanics
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