A Primer on Pontryagin's Principle in Optimal Control

A Primer on Pontryagin's Principle in Optimal Control

Author: I. Michael Ross

Publisher:

Published: 2015-03-03

Total Pages: 370

ISBN-13: 9780984357116

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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. The style of the book is easygoing and engaging. The classical calculus of variations is an unnecessary prerequisite for understanding optimal control theory. Ross uses original references to weave an entertaining historical account of various events. Students, particularly beginners, will embark on a minimum-time trajectory to applying Pontryagin's Principle.


Optimal Control with Engineering Applications

Optimal Control with Engineering Applications

Author: Hans P. Geering

Publisher: Springer Science & Business Media

Published: 2007-03-23

Total Pages: 141

ISBN-13: 3540694382

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This book introduces a variety of problem statements in classical optimal control, in optimal estimation and filtering, and in optimal control problems with non-scalar-valued performance criteria. Many example problems are solved completely in the body of the text. All chapter-end exercises are sketched in the appendix. The theoretical part of the book is based on the calculus of variations, so the exposition is very transparent and requires little mathematical rigor.


Automotive Model Predictive Control

Automotive Model Predictive Control

Author: Luigi Del Re

Publisher: Springer

Published: 2010-03-11

Total Pages: 291

ISBN-13: 1849960712

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Automotive control has developed over the decades from an auxiliary te- nology to a key element without which the actual performances, emission, safety and consumption targets could not be met. Accordingly, automotive control has been increasing its authority and responsibility – at the price of complexity and di?cult tuning. The progressive evolution has been mainly ledby speci?capplicationsandshorttermtargets,withthe consequencethat automotive control is to a very large extent more heuristic than systematic. Product requirements are still increasing and new challenges are coming from potentially huge markets like India and China, and against this ba- ground there is wide consensus both in the industry and academia that the current state is not satisfactory. Model-based control could be an approach to improve performance while reducing development and tuning times and possibly costs. Model predictive control is a kind of model-based control design approach which has experienced a growing success since the middle of the 1980s for “slow” complex plants, in particular of the chemical and process industry. In the last decades, severaldevelopments haveallowedusing these methods also for “fast”systemsandthis hassupporteda growinginterestinitsusealsofor automotive applications, with several promising results reported. Still there is no consensus on whether model predictive control with its high requi- ments on model quality and on computational power is a sensible choice for automotive control.


Optimal Control Theory

Optimal Control Theory

Author: Suresh P. Sethi

Publisher: Taylor & Francis US

Published: 2006

Total Pages: 536

ISBN-13: 9780387280929

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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.


Optimal Control

Optimal Control

Author: Michael Athans

Publisher: Courier Corporation

Published: 2013-04-26

Total Pages: 900

ISBN-13: 0486318184

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Geared toward advanced undergraduate 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. Rather than presenting an exhaustive treatise, Optimal Control offers a detailed introduction that fosters careful thinking and disciplined intuition. It develops the basic mathematical background, with a coherent formulation of the control problem and discussions of the necessary conditions for optimality based on the maximum principle of Pontryagin. In-depth examinations cover applications of the theory to minimum time, minimum fuel, and to quadratic criteria problems. The structure, properties, and engineering realizations of several optimal feedback control systems also receive attention. Special features include numerous specific problems, carried through to engineering realization in block diagram form. The text treats almost all current examples of control problems that permit analytic solutions, and its unified approach makes frequent use of geometric ideas to encourage students' intuition.


Optimal Control: Novel Directions and Applications

Optimal Control: Novel Directions and Applications

Author: Daniela Tonon

Publisher: Springer

Published: 2017-09-01

Total Pages: 399

ISBN-13: 3319607715

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Focusing on applications to science and engineering, this book presents the results of the ITN-FP7 SADCO network’s innovative research in optimization and control in the following interconnected topics: optimality conditions in optimal control, dynamic programming approaches to optimal feedback synthesis and reachability analysis, and computational developments in model predictive control. The novelty of the book resides in the fact that it has been developed by early career researchers, providing a good balance between clarity and scientific rigor. Each chapter features an introduction addressed to PhD students and some original contributions aimed at specialist researchers. Requiring only a graduate mathematical background, the book is self-contained. It will be of particular interest to graduate and advanced undergraduate students, industrial practitioners and to senior scientists wishing to update their knowledge.


Functional Analysis, Calculus of Variations and Optimal Control

Functional Analysis, Calculus of Variations and Optimal Control

Author: Francis Clarke

Publisher: Springer Science & Business Media

Published: 2013-02-06

Total Pages: 589

ISBN-13: 1447148207

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Functional analysis owes much of its early impetus to problems that arise in the calculus of variations. In turn, the methods developed there have been applied to optimal control, an area that also requires new tools, such as nonsmooth analysis. This self-contained textbook gives a complete course on all these topics. It is written by a leading specialist who is also a noted expositor. This book provides a thorough introduction to functional analysis and includes many novel elements as well as the standard topics. A short course on nonsmooth analysis and geometry completes the first half of the book whilst the second half concerns the calculus of variations and optimal control. The author provides a comprehensive course on these subjects, from their inception through to the present. A notable feature is the inclusion of recent, unifying developments on regularity, multiplier rules, and the Pontryagin maximum principle, which appear here for the first time in a textbook. Other major themes include existence and Hamilton-Jacobi methods. The many substantial examples, and the more than three hundred exercises, treat such topics as viscosity solutions, nonsmooth Lagrangians, the logarithmic Sobolev inequality, periodic trajectories, and systems theory. They also touch lightly upon several fields of application: mechanics, economics, resources, finance, control engineering. Functional Analysis, Calculus of Variations and Optimal Control is intended to support several different courses at the first-year or second-year graduate level, on functional analysis, on the calculus of variations and optimal control, or on some combination. For this reason, it has been organized with customization in mind. The text also has considerable value as a reference. Besides its advanced results in the calculus of variations and optimal control, its polished presentation of certain other topics (for example convex analysis, measurable selections, metric regularity, and nonsmooth analysis) will be appreciated by researchers in these and related fields.


Optimal Control of Nonlinear Processes

Optimal Control of Nonlinear Processes

Author: Dieter Grass

Publisher: Springer Science & Business Media

Published: 2008-07-24

Total Pages: 552

ISBN-13: 3540776478

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Dynamic optimization is rocket science – and more. This volume teaches researchers and students alike to harness the modern theory of dynamic optimization to solve practical problems. These problems not only cover those in space flight, but also in emerging social applications such as the control of drugs, corruption, and terror. This volume is designed to be a lively introduction to the mathematics and a bridge to these hot topics in the economics of crime for current scholars. The authors celebrate Pontryagin’s Maximum Principle – that crowning intellectual achievement of human understanding. The rich theory explored here is complemented by numerical methods available through a companion web site.


Optimal Control Theory with Applications in Economics

Optimal Control Theory with Applications in Economics

Author: Thomas A. Weber

Publisher: MIT Press

Published: 2011-09-30

Total Pages: 387

ISBN-13: 0262015730

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A rigorous introduction to optimal control theory, with an emphasis on applications in economics. This book bridges optimal control theory and economics, discussing ordinary differential equations, optimal control, game theory, and mechanism design in one volume. Technically rigorous and largely self-contained, it provides an introduction to the use of optimal control theory for deterministic continuous-time systems in economics. The theory of ordinary differential equations (ODEs) is the backbone of the theory developed in the book, and chapter 2 offers a detailed review of basic concepts in the theory of ODEs, including the solution of systems of linear ODEs, state-space analysis, potential functions, and stability analysis. Following this, the book covers the main results of optimal control theory, in particular necessary and sufficient optimality conditions; game theory, with an emphasis on differential games; and the application of control-theoretic concepts to the design of economic mechanisms. Appendixes provide a mathematical review and full solutions to all end-of-chapter problems. The material is presented at three levels: single-person decision making; games, in which a group of decision makers interact strategically; and mechanism design, which is concerned with a designer's creation of an environment in which players interact to maximize the designer's objective. The book focuses on applications; the problems are an integral part of the text. It is intended for use as a textbook or reference for graduate students, teachers, and researchers interested in applications of control theory beyond its classical use in economic growth. The book will also appeal to readers interested in a modeling approach to certain practical problems involving dynamic continuous-time models.


Introduction to Optimal Control Theory

Introduction to Optimal Control Theory

Author: Jack Macki

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 179

ISBN-13: 1461256712

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This monograph is an introduction to optimal control theory for systems governed by vector ordinary differential equations. It is not intended as a state-of-the-art handbook for researchers. We have tried to keep two types of reader in mind: (1) mathematicians, graduate students, and advanced undergraduates in mathematics who want a concise introduction to a field which contains nontrivial interesting applications of mathematics (for example, weak convergence, convexity, and the theory of ordinary differential equations); (2) economists, applied scientists, and engineers who want to understand some of the mathematical foundations. of optimal control theory. In general, we have emphasized motivation and explanation, avoiding the "definition-axiom-theorem-proof" approach. We make use of a large number of examples, especially one simple canonical example which we carry through the entire book. In proving theorems, we often just prove the simplest case, then state the more general results which can be proved. Many of the more difficult topics are discussed in the "Notes" sections at the end of chapters and several major proofs are in the Appendices. We feel that a solid understanding of basic facts is best attained by at first avoiding excessive generality. We have not tried to give an exhaustive list of references, preferring to refer the reader to existing books or papers with extensive bibliographies. References are given by author's name and the year of publication, e.g., Waltman [1974].