Optimization and Optimal Control

Proceedings of a Conference held at Oberwolfach, November 17-23, 1974
Author: R. Bulirsch,W. Oettli,J. Stoer
Publisher: Springer
ISBN: 3540375910
Category: Mathematics
Page: 298
View: 6379

Continue Reading →

Optimal Control

An Introduction to the Theory with Applications
Author: Leslie M. Hocking
Publisher: Oxford University Press
ISBN: 9780198596820
Category: Mathematics
Page: 254
View: 8836

Continue Reading →

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


Author: Richard Vinter
Publisher: Springer Science & Business Media
ISBN: 9780817640750
Category: Science
Page: 500
View: 3265

Continue Reading →

“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

Optimal Control


Author: Frank L. Lewis,Vassilis L. Syrmos
Publisher: John Wiley & Sons
ISBN: 9780471033783
Category: Technology & Engineering
Page: 541
View: 3881

Continue Reading →

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 Theory

An Introduction
Author: Donald E. Kirk
Publisher: Courier Corporation
ISBN: 0486135071
Category: Technology & Engineering
Page: 480
View: 5379

Continue Reading →

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 Systems


Author: D. Subbaram Naidu
Publisher: CRC Press
ISBN: 9780849308925
Category: Technology & Engineering
Page: 464
View: 5402

Continue Reading →

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
Author: A. E. Bryson
Publisher: CRC Press
ISBN: 9780891162285
Category: Technology & Engineering
Page: 496
View: 5616

Continue Reading →

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, Stabilization and Nonsmooth Analysis


Author: Marcio S. de Queiroz,Michael Malisoff,Peter Wolenski
Publisher: Springer Science & Business Media
ISBN: 9783540213307
Category: Technology & Engineering
Page: 361
View: 3578

Continue Reading →

This edited book contains selected papers presented at the Louisiana Conference on Mathematical Control Theory (MCT'03), which brought together over 35 prominent world experts in mathematical control theory and its applications. The book forms a well-integrated exploration of those areas of mathematical control theory in which nonsmooth analysis is having a major impact. These include necessary and sufficient conditions in optimal control, Lyapunov characterizations of stability, input-to-state stability, the construction of feedback mechanisms, viscosity solutions of Hamilton-Jacobi equations, invariance, approximation theory, impulsive systems, computational issues for nonlinear systems, and other topics of interest to mathematicians and control engineers. The book has a strong interdisciplinary component and was designed to facilitate the interaction between leading mathematical experts in nonsmooth analysis and engineers who are increasingly using nonsmooth analytic tools.

Optimal Control and Estimation


Author: Robert F. Stengel
Publisher: Courier Corporation
ISBN: 0486134814
Category: Mathematics
Page: 672
View: 5776

Continue Reading →

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

Optimal Control Theory for Applications


Author: David G. Hull
Publisher: Springer Science & Business Media
ISBN: 9780387400709
Category: Technology & Engineering
Page: 384
View: 3578

Continue Reading →

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 of Nonlinear Parabolic Systems

Theory: Algorithms and Applications
Author: Pekka Neittaanmaki,D. Tiba
Publisher: CRC Press
ISBN: 9780824790813
Category: Mathematics
Page: 424
View: 5261

Continue Reading →

This book discusses theoretical approaches to the study of optimal control problems governed by non-linear evolutions - including semi-linear equations, variational inequalities and systems with phase transitions. It also provides algorithms for solving non-linear parabolic systems and multiphase Stefan-like systems.

Numerical Methods for Optimal Control Problems with State Constraints


Author: Radoslaw Pytlak
Publisher: Springer
ISBN: 3540486623
Category: Science
Page: 218
View: 4166

Continue Reading →

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
Author: Rolf Klötzler
Publisher: Springer Science & Business Media
ISBN: 9783764359065
Category: Mathematics
Page: 340
View: 3987

Continue Reading →

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


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: 9072

Continue Reading →

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
Author: Arturo Locatelli
Publisher: Springer Science & Business Media
ISBN: 9783764364083
Category: Language Arts & Disciplines
Page: 294
View: 5641

Continue Reading →

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

Linear Quadratic Methods
Author: Brian D. O. Anderson,John B. Moore
Publisher: Courier Corporation
ISBN: 0486457664
Category: Technology & Engineering
Page: 448
View: 321

Continue Reading →

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.

Optimal Control Models in Finance

A New Computational Approach
Author: Ping Chen,Sardar M. N. Islam
Publisher: Springer Science & Business Media
ISBN: 0387235701
Category: Mathematics
Page: 201
View: 9143

Continue Reading →

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.

Robust Control Design: An Optimal Control Approach


Author: Feng Lin
Publisher: John Wiley & Sons
ISBN: 9780470059562
Category: Science
Page: 378
View: 3439

Continue Reading →

Comprehensive and accessible guide to the three main approaches to robust control design and its applications Optimal control is a mathematical field that is concerned with control policies that can be deduced using optimization algorithms. The optimal control approach to robust control design differs from conventional direct approaches to robust control that are more commonly discussed by firstly translating the robust control problem into its optimal control counterpart, and then solving the optimal control problem. Robust Control Design: An Optimal Control Approach offers a complete presentation of this approach to robust control design, presenting modern control theory in an concise manner. The other two major approaches to robust control design, the H_infinite approach and the Kharitonov approach, are also covered and described in the simplest terms possible, in order to provide a complete overview of the area. It includes up-to-date research, and offers both theoretical and practical applications that include flexible structures, robotics, and automotive and aircraft control. Robust Control Design: An Optimal Control Approach will be of interest to those needing an introductory textbook on robust control theory, design and applications as well as graduate and postgraduate students involved in systems and control research. Practitioners will also find the applications presented useful when solving practical problems in the engineering field.

Calculus of Variations and Optimal Control


Author: N. P. Osmolovskii
Publisher: American Mathematical Soc.
ISBN: 9780821897874
Category: Calculus of variations
Page: 372
View: 7130

Continue Reading →

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.