Optimization and Optimal Control

Proceedings of a Conference held at Oberwolfach, November 17-23, 1974

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Author: R. Bulirsch,W. Oettli,J. Stoer

Publisher: Springer

ISBN: 3540375910

Category: Mathematics

Page: 298

View: 3468

Optimal Control Theory

An Introduction

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Author: Donald E. Kirk

Publisher: Courier Corporation

ISBN: 0486135071

Category: Technology & Engineering

Page: 480

View: 978

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 Control and Estimation

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Author: Robert F. Stengel

Publisher: Courier Corporation

ISBN: 0486134814

Category: Mathematics

Page: 672

View: 7225

Graduate-level text provides introduction to optimal control theory for stochastic systems, emphasizing application of basic concepts to real problems.

Optimal Control

An Introduction to the Theory with Applications

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Author: Leslie M. Hocking

Publisher: Oxford University Press

ISBN: 9780198596820

Category: Mathematics

Page: 254

View: 9642

This textbook is a straightforward introduction to the theory of optimal control with an emphasis on presenting many different applications. Included are many worked examples and numerous exercises.

Optimal Control

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Author: Frank L. Lewis,Vassilis L. Syrmos

Publisher: John Wiley & Sons

ISBN: 9780471033783

Category: Technology & Engineering

Page: 541

View: 1595

This new, updated edition of Optimal Control reflects major changes that have occurred in the field in recent years and presents, in a clear and direct way, the fundamentals of optimal control theory. It covers the major topics involving measurement, principles of optimality, dynamic programming, variational methods, Kalman filtering, and other solution techniques. To give the reader a sense of the problems that can arise in a hands–on project, the authors have included new material on optimal output feedback control, a technique used in the aerospace industry. Also included are two new chapters on robust control to provide background in this rapidly growing area of interest. Relations to classical control theory are emphasized throughout the text, and a root–locus approach to steady–state controller design is included. A chapter on optimal control of polynomial systems is designed to give the reader sufficient background for further study in the field of adaptive control. The authors demonstrate through numerous examples that computer simulations of optimal controllers are easy to implement and help give the reader an intuitive feel for the equations. To help build the reader′s confidence in understanding the theory and its practical applications, the authors have provided many opportunities throughout the book for writing simple programs. Optimal Control will also serve as an invaluable reference for control engineers in the industry. It offers numerous tables that make it easy to find the equations needed to implement optimal controllers for practical applications. All simulations have been performed using MATLAB and relevant Toolboxes. Optimal Control assumes a background in the state–variable representation of systems; because matrix manipulations are the basic mathematical vehicle of the book, a short review is included in the appendix. A lucid introductory text and an invaluable reference, Optimal Control will serve as a complete tool for the professional engineer and advanced student alike. 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. Its coverage encompasses all the fundamental topics as well as the major changes of recent years, including output–feedback design and robust design. An abundance of computer simulations using MATLAB and relevant Toolboxes is included to give the reader the actual experience of applying the theory to real–world situations. Major topics covered include: ∗ Static Optimization ∗ Optimal Control of Discrete–Time Systems ∗ Optimal Control of Continuous–Time Systems ∗ The Tracking Problem and Other LQR Extensions ∗ Final–Time–Free and Constrained Input Control ∗ Dynamic Programming ∗ Optimal Control for Polynomial Systems ∗ Output Feedback and Structured Control ∗ Robustness and Multivariable Frequency–Domain Techniques

Optimal Control Systems

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Author: D. Subbaram Naidu

Publisher: CRC Press

ISBN: 9780849308925

Category: Technology & Engineering

Page: 464

View: 2961

The theory of optimal control systems has grown and flourished since the 1960's. Many texts, written on varying levels of sophistication, have been published on the subject. Yet even those purportedly designed for beginners in the field are often riddled with complex theorems, and many treatments fail to include topics that are essential to a thorough grounding in the various aspects of and approaches to optimal control. Optimal Control Systems provides a comprehensive but accessible treatment of the subject with just the right degree of mathematical rigor to be complete but practical. It provides a solid bridge between "traditional" optimization using the calculus of variations and what is called "modern" optimal control. It also treats both continuous-time and discrete-time optimal control systems, giving students a firm grasp on both methods. Among this book's most outstanding features is a summary table that accompanies each topic or problem and includes a statement of the problem with a step-by-step solution. Students will also gain valuable experience in using industry-standard MATLAB and SIMULINK software, including the Control System and Symbolic Math Toolboxes. Diverse applications across fields from power engineering to medicine make a foundation in optimal control systems an essential part of an engineer's background. This clear, streamlined presentation is ideal for a graduate level course on control systems and as a quick reference for working engineers.

Applied Optimal Control

Optimization, Estimation and Control

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Author: A. E. Bryson

Publisher: CRC Press

ISBN: 9780891162285

Category: Technology & Engineering

Page: 496

View: 8348

This best-selling text focuses on the analysis and design of complicated dynamics systems. CHOICE called it “a high-level, concise book that could well be used as a reference by engineers, applied mathematicians, and undergraduates. The format is good, the presentation clear, the diagrams instructive, the examples and problems helpful...References and a multiple-choice examination are included.”

Optimal Control Theory for Applications

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Author: David G. Hull

Publisher: Springer Science & Business Media

ISBN: 9780387400709

Category: Technology & Engineering

Page: 384

View: 389

The published material represents the outgrowth of teaching analytical optimization to aerospace engineering graduate students. To make the material available to the widest audience, the prerequisites are limited to calculus and differential equations. It is also a book about the mathematical aspects of optimal control theory. It was developed in an engineering environment from material learned by the author while applying it to the solution of engineering problems. One goal of the book is to help engineering graduate students learn the fundamentals which are needed to apply the methods to engineering problems. The examples are from geometry and elementary dynamical systems so that they can be understood by all engineering students. Another goal of this text is to unify optimization by using the differential of calculus to create the Taylor series expansions needed to derive the optimality conditions of optimal control theory.

Optimal Control

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Author: Richard Vinter

Publisher: Springer Science & Business Media

ISBN: 9780817640750

Category: Science

Page: 500

View: 4493

“Each chapter contains a well-written introduction and notes. They include the author's deep insights on the subject matter and provide historical comments and guidance to related literature. This book may well become an important milestone in the literature of optimal control." —Mathematical Reviews “Thanks to a great effort to be self-contained, [this book] renders accessibly the subject to a wide audience. Therefore, it is recommended to all researchers and professionals interested in Optimal Control and its engineering and economic applications. It can serve as an excellent textbook for graduate courses in Optimal Control (with special emphasis on Nonsmooth Analysis)." —Automatica

Numerical Methods for Optimal Control Problems with State Constraints

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Author: Radoslaw Pytlak

Publisher: Springer

ISBN: 3540486623

Category: Science

Page: 218

View: 381

While optimality conditions for optimal control problems with state constraints have been extensively investigated in the literature the results pertaining to numerical methods are relatively scarce. This book fills the gap by providing a family of new methods. Among others, a novel convergence analysis of optimal control algorithms is introduced. The analysis refers to the topology of relaxed controls only to a limited degree and makes little use of Lagrange multipliers corresponding to state constraints. This approach enables the author to provide global convergence analysis of first order and superlinearly convergent second order methods. Further, the implementation aspects of the methods developed in the book are presented and discussed. The results concerning ordinary differential equations are then extended to control problems described by differential-algebraic equations in a comprehensive way for the first time in the literature.

Variational Calculus, Optimal Control, and Applications

International Conference in Honour of L. Bittner and R. Klèotzler, Trassenheide, Germany, September 23-27, 1996

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Author: Rolf Klötzler

Publisher: Springer Science & Business Media

ISBN: 9783764359065

Category: Mathematics

Page: 340

View: 8457

Variational Calculus, Optimal Control and Applications was the topic of the 12th Baltic Sea conference, traditionally an important meeting place for scientists from Eastern and Western Europe as well as the USA. This work contains contributions presented at that conference and addresses four problem complexes mostly motivated by practical problems. The starting points are often questions taken from flight dynamics. The first chapter deals with existence theory and optimality conditions needed for justification of, and used in, numerical algorithms. Analysis and synthesis of control systems and dynamic programming are presented in the second chapter. A modern interpretation of a solution of the Hamilton-Jacobi-Bellman equation is given. This is closely connected to the question of real-time or feedback control. Recent advances in the field of numerical methods and their applications to flight path optimization and fluid dynamics follow. The reader will find nonlinear programming methods, accelerated multiple shooting, homotopy and SQP methods. A wide variety of applications to mechanical and aerospace systems concludes this work: space flight problems, mobile robot controlling, geometrical extremal problems, fluid transport, fluid waves and human sciences.

Optimal Control Theory and Static Optimization in Economics

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Author: Daniel Léonard,Ngo van Long,Ngo van (McGill University Long, Montreal),Ngo, Van Long

Publisher: Cambridge University Press

ISBN: 9780521337465

Category: Business & Economics

Page: 353

View: 4091

Optimal control theory is a technique being used increasingly by academic economists to study problems involving optimal decisions in a multi-period framework. This book is designed to make the difficult subject of optimal control theory easily accessible to economists while at the same time maintaining rigor. 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. The development of the text is gradual and fully integrated, beginning with the simple formulations and progressing to advanced topics. Optimal control theory is introduced directly, without recourse to the calculus of variations, and the connection with the latter and with dynamic programming is explained in a separate chapter. Also, the book draws the parallel between optimal control theory and static optimization. No previous knowledge of differential equations is required.

Optimal Control

An Introduction

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Author: Arturo Locatelli

Publisher: Springer Science & Business Media

ISBN: 9783764364083

Category: Language Arts & Disciplines

Page: 294

View: 2135

From the very beginning in the late 1950s of the basic ideas of optimal control, attitudes toward the topic in the scientific and engineering community have ranged from an excessive enthusiasm for its reputed capability ofsolving almost any kind of problem to an (equally) unjustified rejection of it as a set of abstract mathematical concepts with no real utility. The truth, apparently, lies somewhere between these two extremes. Intense research activity in the field of optimization, in particular with reference to robust control issues, has caused it to be regarded as a source of numerous useful, powerful, and flexible tools for the control system designer. The new stream of research is deeply rooted in the well-established framework of linear quadratic gaussian control theory, knowledge ofwhich is an essential requirement for a fruitful understanding of optimization. In addition, there appears to be a widely shared opinion that some results of variational techniques are particularly suited for an approach to nonlinear solutions for complex control problems. For these reasons, even though the first significant achievements in the field were published some forty years ago, a new presentation ofthe basic elements ofclassical optimal control theory from a tutorial point of view seems meaningful and contemporary. This text draws heavily on the content ofthe Italian language textbook "Con trollo ottimo" published by Pitagora and used in a number of courses at the Politec nico of Milan.

Optimal Control Models in Finance

A New Computational Approach

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Author: Ping Chen,Sardar M. N. Islam

Publisher: Springer Science & Business Media

ISBN: 0387235701

Category: Mathematics

Page: 201

View: 1329

This book reports initial efforts in providing some useful extensions in - nancial modeling; further work is necessary to complete the research agenda. The demonstrated extensions in this book in the computation and modeling of optimal control in finance have shown the need and potential for further areas of study in financial modeling. Potentials are in both the mathematical structure and computational aspects of dynamic optimization. There are needs for more organized and coordinated computational approaches. These ext- sions will make dynamic financial optimization models relatively more stable for applications to academic and practical exercises in the areas of financial optimization, forecasting, planning and optimal social choice. This book will be useful to graduate students and academics in finance, mathematical economics, operations research and computer science. Prof- sional practitioners in the above areas will find the book interesting and inf- mative. The authors thank Professor B.D. Craven for providing extensive guidance and assistance in undertaking this research. This work owes significantly to him, which will be evident throughout the whole book. The differential eq- tion solver “nqq” used in this book was first developed by Professor Craven. Editorial assistance provided by Matthew Clarke, Margarita Kumnick and Tom Lun is also highly appreciated. Ping Chen also wants to thank her parents for their constant support and love during the past four years.

Optimal Control

Linear Quadratic Methods

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Author: Brian D. O. Anderson,John B. Moore

Publisher: Courier Corporation

ISBN: 0486457664

Category: Technology & Engineering

Page: 448

View: 497

Numerous examples highlight this treatment of the use of linear quadratic Gaussian methods for control system design. It explores linear optimal control theory from an engineering viewpoint, with illustrations of practical applications. Key topics include loop-recovery techniques, frequency shaping, and controller reduction. Numerous examples and complete solutions. 1990 edition.

Calculus of Variations and Optimal Control

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Author: N. P. Osmolovskii

Publisher: American Mathematical Soc.

ISBN: 9780821897874

Category: Calculus of variations

Page: 372

View: 2737

The theory of a Pontryagin minimum is developed for problems in the calculus of variations. The application of the notion of a Pontryagin minimum to the calculus of variations is a distinctive feature of this book. A new theory of quadratic conditions for a Pontryagin minimum, which covers broken extremals, is developed, and corresponding sufficient conditions for a strong minimum are obtained. Some classical theorems of the calculus of variations are generalized.

Nonlinear and Optimal Control Theory

Lectures Given at the C.I.M.E. Summer School Held in Cetraro, Italy, June 19-29, 2004

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Author: Andrei A. Agrachev,A. Stephen Morse,Eduardo D. Sontag,Hector J. Sussmann,Vadim I. Utkin

Publisher: Springer Science & Business Media

ISBN: 3540776443

Category: Language Arts & Disciplines

Page: 351

View: 4936

The lectures gathered in this volume present some of the different aspects of Mathematical Control Theory. Adopting the point of view of Geometric Control Theory and of Nonlinear Control Theory, the lectures focus on some aspects of the Optimization and Control of nonlinear, not necessarily smooth, dynamical systems. Specifically, three of the five lectures discuss respectively: logic-based switching control, sliding mode control and the input to the state stability paradigm for the control and stability of nonlinear systems. The remaining two lectures are devoted to Optimal Control: one investigates the connections between Optimal Control Theory, Dynamical Systems and Differential Geometry, while the second presents a very general version, in a non-smooth context, of the Pontryagin Maximum Principle. The arguments of the whole volume are self-contained and are directed to everyone working in Control Theory. They offer a sound presentation of the methods employed in the control and optimization of nonlinear dynamical systems.

Optimal Control of Coupled Systems of Partial Differential Equations

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Author: Karl Kunisch,Günter Leugering,Jürgen Sprekels,Fredi Tröltzsch

Publisher: Springer Science & Business Media

ISBN: 9783764389239

Category: Mathematics

Page: 345

View: 9228

Contains contributions originating from the 'Conference on Optimal Control of Coupled Systems of Partial Differential Equations', held at the 'Mathematisches Forschungsinstitut Oberwolfach' in March 2008. This work covers a range of topics such as controllability, optimality systems, model-reduction techniques, and fluid-structure interactions.

The Calculus of Variations and Optimal Control

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Author: George Leitmann

Publisher: Springer Science & Business Media

ISBN: 9780306407079

Category: Mathematics

Page: 311

View: 5274

When the Tyrian princess Dido landed on the North African shore of the Mediterranean sea she was welcomed by a local chieftain. He offered her all the land that she could enclose between the shoreline and a rope of knotted cowhide. While the legend does not tell us, we may assume that Princess Dido arrived at the correct solution by stretching the rope into the shape of a circular arc and thereby maximized the area of the land upon which she was to found Carthage. This story of the founding of Carthage is apocryphal. Nonetheless it is probably the first account of a problem of the kind that inspired an entire mathematical discipline, the calculus of variations and its extensions such as the theory of optimal control. 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. The discussion in Part I is restricted to the simplest problem of the calculus of variations. The topic is entirely classical; all of the basic theory had been developed before the turn of the century. Consequently the material comes from many sources; however, those most useful to me have been the books of Oskar Bolza and of George M. Ewing. Part II is devoted to the elementary aspects of the modern extension of the calculus of variations, the theory of optimal control of dynamical systems.