Dynamic Programming and Optimal Control

Author: Dimitri P. Bertsekas

Publisher: N.A

ISBN: 9781886529304

Category: Mathematics

Page: 445

View: 3744

"The leading and most up-to-date textbook on the far-ranging algorithmic methododogy of Dynamic Programming, which can be used for optimal control, Markovian decision problems, planning and sequential decision making under uncertainty, and discrete/combinatorial optimization. The treatment focuses on basic unifying themes, and conceptual foundations. It illustrates the versatility, power, and generality of the method with many examples and applications from engineering, operations research, and other fields. It also addresses extensively the practical application of the methodology, possibly through the use of approximations, and provides an extensive treatment of the far-reaching methodology of Neuro-Dynamic Programming/Reinforcement Learning. The first volume is oriented towards modeling, conceptualization, and finite-horizon problems, but also includes a substantive introduction to infinite horizon problems that is suitable for classroom use. The second volume is oriented towards mathematical analysis and computation, treats infinite horizon problems extensively, and provides an up-to-date account of approximate large-scale dynamic programming and reinforcement learning. The text contains many illustrations, worked-out examples, and exercises."--Publisher's website.

Dynamic Programming

Models and Applications

Author: Eric V. Denardo

Publisher: Courier Corporation

ISBN: 0486150852

Category: Technology & Engineering

Page: 240

View: 4308

Introduction to sequential decision processes covers use of dynamic programming in studying models of resource allocation, methods for approximating solutions of control problems in continuous time, production control, more. 1982 edition.

Dynamic Programming and Its Application to Optimal Control

Author: N.A

Publisher: Elsevier

ISBN: 9780080955896

Category: Mathematics

Page: 322

View: 5917

In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering

Linear Network Optimization

Algorithms and Codes

Author: Dimitri P. Bertsekas

Publisher: MIT Press

ISBN: 9780262023344

Category: Business & Economics

Page: 359

View: 3746

Large-scale optimization is becoming increasingly important for students and professionals in electrical and industrial engineering, computer science, management science and operations research, and applied mathematics. Linear Network Optimization presents a thorough treatment of classical approaches to network problems such as shortest path, max-flow, assignment, transportation, and minimum cost flow problems. It is the first text to clearly explain important recent algorithms such as auction and relaxation, proposed by the author and others for the solution of these problems. Its coverage of both theory and implementations make it particularly useful as a text for a graduate-level course on network optimization as well as a practical guide to state-of-the-art codes in the field. Bertsekas focuses on the algorithms that have proved successful in practice and provides FORTRAN codes that implement them. The presentation is clear, mathematically rigorous, and economical. Many illustrations, examples, and exercises are included in the text. Dimitri P. Bertsekas is Professor of Electrical Engineering and Computer Science at MIT. Contents: Introduction. Simplex Methods. Dual Ascent Methods. Auction Algorithms. Performance and Comparisons. Appendixes.

Dynamic Programming

Foundations and Principles, Second Edition

Author: Moshe Sniedovich

Publisher: CRC Press

ISBN: 9781420014631

Category: Business & Economics

Page: 624

View: 9406

Incorporating a number of the author’s recent ideas and examples, Dynamic Programming: Foundations and Principles, Second Edition presents a comprehensive and rigorous treatment of dynamic programming. The author emphasizes the crucial role that modeling plays in understanding this area. He also shows how Dijkstra’s algorithm is an excellent example of a dynamic programming algorithm, despite the impression given by the computer science literature. New to the Second Edition Expanded discussions of sequential decision models and the role of the state variable in modeling A new chapter on forward dynamic programming models A new chapter on the Push method that gives a dynamic programming perspective on Dijkstra’s algorithm for the shortest path problem A new appendix on the Corridor method Taking into account recent developments in dynamic programming, this edition continues to provide a systematic, formal outline of Bellman’s approach to dynamic programming. It looks at dynamic programming as a problem-solving methodology, identifying its constituent components and explaining its theoretical basis for tackling problems.

Optimal Control Theory

An Introduction

Author: Donald E. Kirk

Publisher: Courier Corporation

ISBN: 0486135071

Category: Technology & Engineering

Page: 480

View: 7523

Upper-level undergraduate text introduces aspects of optimal control theory: dynamic programming, Pontryagin's minimum principle, and numerical techniques for trajectory optimization. Numerous figures, tables. Solution guide available upon request. 1970 edition.

Optimal Learning

Author: Warren B. Powell,Ilya O. Ryzhov

Publisher: John Wiley & Sons

ISBN: 1118309847

Category: Mathematics

Page: 404

View: 2532

Learn the science of collecting information to make effective decisions Everyday decisions are made without the benefit of accurate information. Optimal Learning develops the needed principles for gathering information to make decisions, especially when collecting information is time-consuming and expensive. Designed for readers with an elementary background in probability and statistics, the book presents effective and practical policies illustrated in a wide range of applications, from energy, homeland security, and transportation to engineering, health, and business. This book covers the fundamental dimensions of a learning problem and presents a simple method for testing and comparing policies for learning. Special attention is given to the knowledge gradient policy and its use with a wide range of belief models, including lookup table and parametric and for online and offline problems. Three sections develop ideas with increasing levels of sophistication: Fundamentals explores fundamental topics, including adaptive learning, ranking and selection, the knowledge gradient, and bandit problems Extensions and Applications features coverage of linear belief models, subset selection models, scalar function optimization, optimal bidding, and stopping problems Advanced Topics explores complex methods including simulation optimization, active learning in mathematical programming, and optimal continuous measurements Each chapter identifies a specific learning problem, presents the related, practical algorithms for implementation, and concludes with numerous exercises. A related website features additional applications and downloadable software, including MATLAB and the Optimal Learning Calculator, a spreadsheet-based package that provides an introduc­tion to learning and a variety of policies for learning.

Robust and Optimal Control

Author: Kemin Zhou,John Comstock Doyle,Keith Glover

Publisher: N.A

ISBN: 9780134565675

Category: Technology & Engineering

Page: 596

View: 7278

For graduate—level courses and for professional reference dealing with robust linear control, multivariable design and H...à Control. Assumes prior knowledge of feedback and control systems and linear systems theory. Also appropriate for practicing engineers familiar with modern control techniques. Class-tested at major institutions around the world and regarded as an “instant classic” by reviewers, this work offers the most complete coverage of robust and H...à control available. The clarity of the overall methodology: how one sets a problem up, introduces uncertainty models, weights, performance norms, etc. set this book apart from others in the field. Offers detailed treatment of topics not found elsewhere including — Riccati equations, ...m theory, H...à loopshaping, controller reduction, how to formulate problems in a LFT form. Key results are given immediately for quick access in the beginning of the book. Overall the book serves as a tremendous self-contained reference by having collected and developed all the important proofs and key results available. Problems sets are available on Internet.

Optimal Control Theory

Applications to Management Science and Economics

Author: Suresh P. Sethi,Gerald L. Thompson

Publisher: Springer Science & Business Media

ISBN: 0387299033

Category: Business & Economics

Page: 506

View: 5142

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. Sethi and Thompson have provided management science and economics communities with a thoroughly revised edition of their classic text on Optimal Control Theory. The new edition has been completely refined with careful attention to the text and graphic material presentation. Chapters cover a range of topics including finance, production and inventory problems, marketing problems, machine maintenance and replacement, problems of optimal consumption of natural resources, and applications of control theory to economics. The book contains new results that were not available when the first edition was published, as well as an expansion of the material on stochastic optimal control theory.

Nonlinear Programming

Author: Dimitri P. Bertsekas

Publisher: N.A

ISBN: 9781886529052

Category: Mathematical optimization

Page: 859

View: 1213

The third edition of the book is a thoroughly rewritten version of the 1999 2nd edition. New material was included, some of the old material was discarded, and a large portion of the remainder was reorganized or revised. This book provides a comprehensive and accessible presentation of algorithms for solving continuous optimization problems. It relies on rigorous mathematical analysis, but also aims at an intuitive exposition that makes use of visualization where possible. It places particular emphasis on modern developments, and their widespread applications in fields such as large-scale resource allocation problems, signal processing, and machine learning. The book was developed through instruction at MIT, focuses on nonlinear and other types of optimization: iterative algorithms for constrained and unconstrained optimization, Lagrange multipliers and duality, large scale problems, and the interface between continuous and discrete optimization. Among its special features, the book: 1) provides extensive coverage of iterative optimization methods within a unifying framework 2) provides a detailed treatment of interior point methods for linear programming 3) covers in depth duality theory from both a variational and a geometrical/convex analysis point of view 4) includes much new material on a number of topics, such as neural network training, large-scale optimization, signal processing, machine learning, and optimal control 5) includes a large number of examples and exercises detailed solutions of many of which are posted on the internet.

Dynamic Programming in Chemical Engineering and Process Control by Sanford M Roberts

Author: Sanford M. Roberts

Publisher: Elsevier

ISBN: 9780080955193

Category: Mathematics

Page: 322

View: 2786

In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering

Applications of Control Theory in Ecology

Proceedings of the Symposium on Optimal Control Theory held at the State University of New York, Syracuse, New York, August 10–16, 1986

Author: Yosef Cohen

Publisher: Springer Science & Business Media

ISBN: 3642466168

Category: Science

Page: 101

View: 9255

Control theory can be roughly classified as deterministic or stochastic. Each of these can further be subdivided into game theory and optimal control theory. The central problem of control theory is the so called constrained maximization (which- with slight modifications--is equivalent to minimization). One can then say, heuristically, that the major problem of control theory is to find the maximum of some performance criterion (or criteria), given a set of constraints. The starting point is, of course, a mathematical representation of the performance criterion (or criteria)- sometimes called the objective functional--along with the constraints. When the objective functional is single valued (Le. , when there is only one objective to be maximized), then one is dealing with optimal control theory. When more than one objective is involved, and the objectives are generally incompatible, then one is dealing with game theory. The first paper deals with stochastic optimal control, using the dynamic programming approach. The next two papers deal with deterministic optimal control, and the final two deal with applications of game theory to ecological problems. In his contribution, Dr. Marc Mangel applies the dynamic proQramming approach, as modified by his recent work--with Dr. Colin Clark, from the University of British Columbia (Mangel and Clark 1987}*--to modelling the "behavioral decisions" of insects. The objective functional is a measure of fitness. Readers interested in detailed development of the subject matter may consult Mangel (1985). My contributions deal with two applications of optimal control theory.