Optimal Control Via Nonsmooth Analysis

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Optimal Control Via Nonsmooth Analysis

Philip Daniel Loewen
Optimal Control Via Nonsmooth Analysis Book PDF

Author : Philip Daniel Loewen
Publisher : American Mathematical Soc.
Page : 112 pages
File Size : 52,5 Mb
Release : 1993
Category : Control theory
ISBN : 0821869965

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Optimal Control Via Nonsmooth Analysis by Philip Daniel Loewen Pdf

This book provides a complete and unified treatment of deterministic problems of dynamic optimization, from the classical themes of the calculus of variations to the forefront of modern research in optimal control. At the heart of the presentation is nonsmooth analysis, a theory of local approximation developed over the last twenty years to provide useful first-order information about sets and functions lying beyond the reach of classical analysis. The book includes an intuitive and geometrically transparent approach to nonsmooth analysis, serving not only to introduce the basic ideas, but also to illuminate the calculations and derivations in the applied sections dealing with the calculus of variations and optimal control. Written in a lively, engaging style and stocked with numerous figures and practice problems, this book offers an ideal introduction to this vigorous field of current research. It is suitable as a graduate text for a one-semester course in optimal control or as a manual for self-study. Each chapter closes with a list of references to ease the reader's transition from active learner to contributing researcher.

Nonsmooth Optimization: Analysis And Algorithms With Applications To Optimal Control

Marko M Makela,Pekka Neittaanmaki
Nonsmooth Optimization Analysis And Algorithms With Applications To Optimal Control Book PDF

Author : Marko M Makela,Pekka Neittaanmaki
Publisher : World Scientific
Page : 268 pages
File Size : 42,9 Mb
Release : 1992-05-07
Category : Mathematics
ISBN : 9789814522410

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Nonsmooth Optimization: Analysis And Algorithms With Applications To Optimal Control by Marko M Makela,Pekka Neittaanmaki Pdf

This book is a self-contained elementary study for nonsmooth analysis and optimization, and their use in solution of nonsmooth optimal control problems. The first part of the book is concerned with nonsmooth differential calculus containing necessary tools for nonsmooth optimization. The second part is devoted to the methods of nonsmooth optimization and their development. A proximal bundle method for nonsmooth nonconvex optimization subject to nonsmooth constraints is constructed. In the last part nonsmooth optimization is applied to problems arising from optimal control of systems covered by partial differential equations. Several practical problems, like process control and optimal shape design problems are considered.

Optimal Control, Stabilization and Nonsmooth Analysis

Marcio S. de Queiroz,Michael Malisoff,Peter Wolenski
Optimal Control Stabilization and Nonsmooth Analysis Book PDF

Author : Marcio S. de Queiroz,Michael Malisoff,Peter Wolenski
Publisher : Springer Science & Business Media
Page : 380 pages
File Size : 48,6 Mb
Release : 2004-04-20
Category : Technology & Engineering
ISBN : 3540213309

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Optimal Control, Stabilization and Nonsmooth Analysis by Marcio S. de Queiroz,Michael Malisoff,Peter Wolenski Pdf

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.

Nonsmooth Analysis and Geometric Methods in Deterministic Optimal Control

Boris S. Mordukhovich,Hector J. Sussmann
Nonsmooth Analysis and Geometric Methods in Deterministic Optimal Control Book PDF

Author : Boris S. Mordukhovich,Hector J. Sussmann
Publisher : Springer Science & Business Media
Page : 256 pages
File Size : 40,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461384892

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Nonsmooth Analysis and Geometric Methods in Deterministic Optimal Control by Boris S. Mordukhovich,Hector J. Sussmann Pdf

This IMA Volume in Mathematics and its Applications NONSMOOTH ANALYSIS AND GEOMETRIC METHODS IN DETERMINISTIC OPTIMAL CONTROL is based on the proceedings of a workshop that was an integral part of the 1992-93 IMA program on "Control Theory. " The purpose of this workshop was to concentrate on powerful mathematical techniques that have been de veloped in deterministic optimal control theory after the basic foundations of the theory (existence theorems, maximum principle, dynamic program ming, sufficiency theorems for sufficiently smooth fields of extremals) were laid out in the 1960s. These advanced techniques make it possible to derive much more detailed information about the structure of solutions than could be obtained in the past, and they support new algorithmic approaches to the calculation of such solutions. We thank Boris S. Mordukhovich and Hector J. Sussmann for organiz ing the workshop and editing the proceedings. We also take this oppor tunity to thank the National Science Foundation and the Army Research Office, whose financial support made the workshop possible. A vner Friedman Willard Miller, Jr. v PREFACE This volume contains the proceedings of the workshop on Nonsmooth Analysis and Geometric Methods in Deterministic Optimal Control held at the Institute for Mathematics and its Applications on February 8-17, 1993 during a special year devoted to Control Theory and its Applications. The workshop-whose organizing committee consisted of V. J urdjevic, B. S. Mordukhovich, R. T. Rockafellar, and H. J.

Nonsmooth Analysis and Control Theory

Francis H. Clarke,Yuri S. Ledyaev,Ronald J. Stern,Peter R. Wolenski
Nonsmooth Analysis and Control Theory Book PDF

Author : Francis H. Clarke,Yuri S. Ledyaev,Ronald J. Stern,Peter R. Wolenski
Publisher : Springer Science & Business Media
Page : 288 pages
File Size : 53,6 Mb
Release : 2008-01-10
Category : Mathematics
ISBN : 9780387226255

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Nonsmooth Analysis and Control Theory by Francis H. Clarke,Yuri S. Ledyaev,Ronald J. Stern,Peter R. Wolenski Pdf

A clear and succinct presentation of the essentials of this subject, together with some of its applications and a generous helping of interesting exercises. Following an introductory chapter with a taste of what is to come, the next three chapters constitute a course in nonsmooth analysis and identify a coherent and comprehensive approach to the subject, leading to an efficient, natural, and powerful body of theory. The whole is rounded off with a self-contained introduction to the theory of control of ordinary differential equations. The authors have incorporated a number of new results which clarify the relationships between the different schools of thought in the subject, with the aim of making nonsmooth analysis accessible to a wider audience. End-of-chapter problems offer scope for deeper understanding.

Optimal Control

Richard Vinter
Optimal Control Book PDF

Author : Richard Vinter
Publisher : Springer Science & Business Media
Page : 500 pages
File Size : 53,5 Mb
Release : 2010-06-25
Category : Science
ISBN : 9780817680862

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Optimal Control by Richard Vinter Pdf

“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

Methods of Dynamic and Nonsmooth Optimization

Frank H. Clarke
Methods of Dynamic and Nonsmooth Optimization Book PDF

Author : Frank H. Clarke
Publisher : SIAM
Page : 95 pages
File Size : 49,9 Mb
Release : 1989-01-01
Category : Mathematics
ISBN : 1611970148

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Methods of Dynamic and Nonsmooth Optimization by Frank H. Clarke Pdf

Presents the elements of a unified approach to optimization based on "nonsmooth analysis," a term introduced in the 1970's by the author, who is a pioneer in the field. Based on a series of lectures given at a conference at Emory University in 1986, this volume presents its subjects in a self-contained and accessible manner. The topics treated here have been in an active state of development, and this work therefore incorporates more recent results than those presented in 1986. Focuses mainly on deterministic optimal control, the calculus of variations, and mathematical programming. In addition, it features a tutorial in nonsmooth analysis and geometry and demonstrates that the method of value function analysis via proximal normals is a powerful tool in the study of necessary conditions, sufficient conditions, controllability, and sensitivity analysis. The distinction between inductive and deductive methods, the use of Hamiltonians, the verification technique, and penalization are also emphasized.

Optimal Control, Stabilization and Nonsmooth Analysis

Marcio S. de Queiroz,Michael Malisoff,Peter Wolenski
Optimal Control Stabilization and Nonsmooth Analysis Book PDF

Author : Marcio S. de Queiroz,Michael Malisoff,Peter Wolenski
Publisher : Springer
Page : 361 pages
File Size : 48,5 Mb
Release : 2014-03-12
Category : Technology & Engineering
ISBN : 3662192934

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Optimal Control, Stabilization and Nonsmooth Analysis by Marcio S. de Queiroz,Michael Malisoff,Peter Wolenski Pdf

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

Richard Vinter
Optimal Control Book PDF

Author : Richard Vinter
Publisher : Springer Science & Business Media
Page : 536 pages
File Size : 48,6 Mb
Release : 2000-05-19
Category : Science
ISBN : 0817640754

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Optimal Control by Richard Vinter Pdf

“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

Functional Analysis, Calculus of Variations and Optimal Control

Francis Clarke
Functional Analysis Calculus of Variations and Optimal Control Book PDF

Author : Francis Clarke
Publisher : Springer Science & Business Media
Page : 589 pages
File Size : 49,5 Mb
Release : 2013-02-06
Category : Mathematics
ISBN : 9781447148203

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Functional Analysis, Calculus of Variations and Optimal Control by Francis Clarke Pdf

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 Nonsmooth Distributed Parameter Systems

Dan Tiba
Optimal Control of Nonsmooth Distributed Parameter Systems Book PDF

Author : Dan Tiba
Publisher : Springer
Page : 176 pages
File Size : 44,8 Mb
Release : 1990
Category : Mathematics
ISBN : UOM:39015049366092

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Optimal Control of Nonsmooth Distributed Parameter Systems by Dan Tiba Pdf

The book is devoted to the study of distributed control problems governed by various nonsmooth state systems. The main questions investigated include: existence of optimal pairs, first order optimality conditions, state-constrained systems, approximation and discretization, bang-bang and regularity properties for optimal control. In order to give the reader a better overview of the domain, several sections deal with topics that do not enter directly into the announced subject: boundary control, delay differential equations. In a subject still actively developing, the methods can be more important than the results and these include: adapted penalization techniques, the singular control systems approach, the variational inequality method, the Ekeland variational principle. Some prerequisites relating to convex analysis, nonlinear operators and partial differential equations are collected in the first chapter or are supplied appropriately in the text. The monograph is intended for graduate students and for researchers interested in this area of mathematics.

Optimization and Nonsmooth Analysis

Frank H. Clarke
Optimization and Nonsmooth Analysis Book PDF

Author : Frank H. Clarke
Publisher : SIAM
Page : 317 pages
File Size : 40,6 Mb
Release : 1990-01-01
Category : Mathematics
ISBN : 9780898712568

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Optimization and Nonsmooth Analysis by Frank H. Clarke Pdf

Mathematical Reviews said of this book that it was 'destined to become a classical reference.' This book has appeared in Russian translation and has been praised both for its lively exposition and its fundamental contributions. The author first develops a general theory of nonsmooth analysis and geometry which, together with a set of associated techniques, has had a profound effect on several branches of analysis and optimization. Clarke then applies these methods to obtain a powerful, unified approach to the analysis of problems in optimal control and mathematical programming. Examples are drawn from economics, engineering, mathematical physics, and various branches of analysis in this reprint volume.

Approximation and Optimization of Discrete and Differential Inclusions

Elimhan N Mahmudov
Approximation and Optimization of Discrete and Differential Inclusions Book PDF

Author : Elimhan N Mahmudov
Publisher : Elsevier
Page : 396 pages
File Size : 45,6 Mb
Release : 2011-08-25
Category : Mathematics
ISBN : 9780123884336

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Approximation and Optimization of Discrete and Differential Inclusions by Elimhan N Mahmudov Pdf

Optimal control theory has numerous applications in both science and engineering. This book presents basic concepts and principles of mathematical programming in terms of set-valued analysis and develops a comprehensive optimality theory of problems described by ordinary and partial differential inclusions. In addition to including well-recognized results of variational analysis and optimization, the book includes a number of new and important ones Includes practical examples

Optimal Control of Nonlinear Processes

Dieter Grass,Jonathan P. Caulkins,Gustav Feichtinger,Gernot Tragler,Doris A. Behrens
Optimal Control of Nonlinear Processes Book PDF

Author : Dieter Grass,Jonathan P. Caulkins,Gustav Feichtinger,Gernot Tragler,Doris A. Behrens
Publisher : Springer Science & Business Media
Page : 552 pages
File Size : 42,9 Mb
Release : 2008-07-24
Category : Business & Economics
ISBN : 9783540776475

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Optimal Control of Nonlinear Processes by Dieter Grass,Jonathan P. Caulkins,Gustav Feichtinger,Gernot Tragler,Doris A. Behrens Pdf

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.

Variational Analysis and Set Optimization

Akhtar A. Khan,Elisabeth Köbis,Christiane Tammer
Variational Analysis and Set Optimization Book PDF

Author : Akhtar A. Khan,Elisabeth Köbis,Christiane Tammer
Publisher : CRC Press
Page : 226 pages
File Size : 41,8 Mb
Release : 2019-06-07
Category : Business & Economics
ISBN : 9781351712064

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Variational Analysis and Set Optimization by Akhtar A. Khan,Elisabeth Köbis,Christiane Tammer Pdf

This book contains the latest advances in variational analysis and set / vector optimization, including uncertain optimization, optimal control and bilevel optimization. Recent developments concerning scalarization techniques, necessary and sufficient optimality conditions and duality statements are given. New numerical methods for efficiently solving set optimization problems are provided. Moreover, applications in economics, finance and risk theory are discussed. Summary The objective of this book is to present advances in different areas of variational analysis and set optimization, especially uncertain optimization, optimal control and bilevel optimization. Uncertain optimization problems will be approached from both a stochastic as well as a robust point of view. This leads to different interpretations of the solutions, which widens the choices for a decision-maker given his preferences. Recent developments regarding linear and nonlinear scalarization techniques with solid and nonsolid ordering cones for solving set optimization problems are discussed in this book. These results are useful for deriving optimality conditions for set and vector optimization problems. Consequently, necessary and sufficient optimality conditions are presented within this book, both in terms of scalarization as well as generalized derivatives. Moreover, an overview of existing duality statements and new duality assertions is given. The book also addresses the field of variable domination structures in vector and set optimization. Including variable ordering cones is especially important in applications such as medical image registration with uncertainties. This book covers a wide range of applications of set optimization. These range from finance, investment, insurance, control theory, economics to risk theory. As uncertain multi-objective optimization, especially robust approaches, lead to set optimization, one main focus of this book is uncertain optimization. Important recent developments concerning numerical methods for solving set optimization problems sufficiently fast are main features of this book. These are illustrated by various examples as well as easy-to-follow-steps in order to facilitate the decision process for users. Simple techniques aimed at practitioners working in the fields of mathematical programming, finance and portfolio selection are presented. These will help in the decision-making process, as well as give an overview of nondominated solutions to choose from.