Download or read book Nonconvex Optimal Control and Variational Problems written by Alexander J. Zaslavski and published by Springer Science & Business Media. This book was released on 2013-06-12 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonconvex Optimal Control and Variational Problems is an important contribution to the existing literature in the field and is devoted to the presentation of progress made in the last 15 years of research in the area of optimal control and the calculus of variations. This volume contains a number of results concerning well-posedness of optimal control and variational problems, nonoccurrence of the Lavrentiev phenomenon for optimal control and variational problems, and turnpike properties of approximate solutions of variational problems. Chapter 1 contains an introduction as well as examples of select topics. Chapters 2-5 consider the well-posedness condition using fine tools of general topology and porosity. Chapters 6-8 are devoted to the nonoccurrence of the Lavrentiev phenomenon and contain original results. Chapter 9 focuses on infinite-dimensional linear control problems, and Chapter 10 deals with “good” functions and explores new understandings on the questions of optimality and variational problems. Finally, Chapters 11-12 are centered around the turnpike property, a particular area of expertise for the author. This volume is intended for mathematicians, engineers, and scientists interested in the calculus of variations, optimal control, optimization, and applied functional analysis, as well as both undergraduate and graduate students specializing in those areas. The text devoted to Turnpike properties may be of particular interest to the economics community.
Download or read book A Variational Approach to Optimal Control of ODEs written by Pablo Pedregal and published by SIAM. This book was released on 2022-07-26 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained book presents in a unified, systematic way the basic principles of optimal control governed by ODEs. Using a variational perspective, the author incorporates important restrictions like constraints for control and state, as well as the state system itself, into the equivalent variational reformulation of the problem. The fundamental issues of existence of optimal solutions, optimality conditions, and numerical approximation are then examined from this variational viewpoint. Inside, readers will find a unified approach to all the basic issues of optimal control, academic and real-world examples testing the book’s variational approach, and a rigorous treatment stressing ideas and arguments rather than the underlying mathematical formalism. A Variational Approach to Optimal Control of ODEs is mainly for applied analysts, applied mathematicians, and control engineers, but will also be helpful to other scientists and engineers who want to understand the basic principles of optimal control governed by ODEs. It requires no prerequisites in variational problems or expertise in numerical approximation. It can be used for a first course in optimal control.
Download or read book Convex Analysis and Variational Problems written by Ivar Ekeland and published by SIAM. This book was released on 1999-12-01 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains different developments of infinite dimensional convex programming in the context of convex analysis, including duality, minmax and Lagrangians, and convexification of nonconvex optimization problems in the calculus of variations (infinite dimension). It also includes the theory of convex duality applied to partial differential equations; no other reference presents this in a systematic way. The minmax theorems contained in this book have many useful applications, in particular the robust control of partial differential equations in finite time horizon. First published in English in 1976, this SIAM Classics in Applied Mathematics edition contains the original text along with a new preface and some additional references.
Download or read book Calculus of Variations and Optimal Control written by Alexander Ioffe and published by CRC Press. This book was released on 2021-02-27 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: The calculus of variations is a classical area of mathematical analysis-300 years old-yet its myriad applications in science and technology continue to hold great interest and keep it an active area of research. These two volumes contain the referenced proceedings of the international conference on Calculus of Variations and Related Topics held at the Technion-Israel Institute of Technology in March 1998. The conference commemorated 300 years of work in the field and brought together many of its leading experts. The papers in the first volume focus on critical point theory and differential equations. The other volume deals with variational aspects of optimal control. Together they provide a unique opportunity to review the state-of-the-art of the calculus of variations, as presented by an international panel of masters in the field.
Download or read book Turnpike Properties in the Calculus of Variations and Optimal Control written by Alexander Zaslavski and published by Springer Science & Business Media. This book was released on 2005-08-25 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the recent progress on the turnpike theory. The turnpike property was discovered by Paul A. Samuelson, who applied it to problems in mathematical economics in 1949. These properties were studied for optimal trajectories of models of economic dynamics determined by convex processes. In this monograph the author, a leading expert in modern turnpike theory, presents a number of results concerning the turnpike properties in the calculus of variations and optimal control which were obtained in the last ten years. These results show that the turnpike properties form a general phenomenon which holds for various classes of variational problems and optimal control problems. The book should help to correct the misapprehension that turnpike properties are only special features of some narrow classes of convex problems of mathematical economics. Audience This book is intended for mathematicians interested in optimal control, calculus of variations, game theory and mathematical economics.
Download or read book Constrained Optimization In The Calculus Of Variations and Optimal Control Theory written by J Gregory and published by CRC Press. This book was released on 2018-01-18 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: The major purpose of this book is to present the theoretical ideas and the analytical and numerical methods to enable the reader to understand and efficiently solve these important optimizational problems.The first half of this book should serve as the major component of a classical one or two semester course in the calculus of variations and optimal control theory. The second half of the book will describe the current research of the authors which is directed to solving these problems numerically. In particular, we present new reformulations of constrained problems which leads to unconstrained problems in the calculus of variations and new general, accurate and efficient numerical methods to solve the reformulated problems. We believe that these new methods will allow the reader to solve important problems.
Download or read book Global Methods in Optimal Control Theory written by Vadim Krotov and published by CRC Press. This book was released on 1995-10-13 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work describes all basic equaitons and inequalities that form the necessary and sufficient optimality conditions of variational calculus and the theory of optimal control. Subjects addressed include developments in the investigation of optimality conditions, new classes of solutions, analytical and computation methods, and applications.
Download or read book Variational Analysis written by R. Tyrrell Rockafellar and published by Springer Science & Business Media. This book was released on 2009-06-26 with total page 747 pages. Available in PDF, EPUB and Kindle. Book excerpt: From its origins in the minimization of integral functionals, the notion of variations has evolved greatly in connection with applications in optimization, equilibrium, and control. This book develops a unified framework and provides a detailed exposition of variational geometry and subdifferential calculus in their current forms beyond classical and convex analysis. Also covered are set-convergence, set-valued mappings, epi-convergence, duality, and normal integrands.
Download or read book Turnpike Properties in the Calculus of Variations and Optimal Control written by Alexander J. Zaslavski and published by Springer Science & Business Media. This book was released on 2006-01-27 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the recent progress on the turnpike theory. The turnpike property was discovered by Paul A. Samuelson, who applied it to problems in mathematical economics in 1949. These properties were studied for optimal trajectories of models of economic dynamics determined by convex processes. In this monograph the author, a leading expert in modern turnpike theory, presents a number of results concerning the turnpike properties in the calculus of variations and optimal control which were obtained in the last ten years. These results show that the turnpike properties form a general phenomenon which holds for various classes of variational problems and optimal control problems. The book should help to correct the misapprehension that turnpike properties are only special features of some narrow classes of convex problems of mathematical economics. Audience This book is intended for mathematicians interested in optimal control, calculus of variations, game theory and mathematical economics.
Download or read book Calculus of Variations and Optimal Control written by N. P. Osmolovskii and published by American Mathematical Soc.. This book was released on 1998-08-18 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Fractional Variational Problems and Optimal Control written by and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Optimal Control of Nonlinear Parabolic Systems written by Pekka Neittaanmaki and published by CRC Press. This book was released on 1994-02-08 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Optimal Control Via Nonsmooth Analysis written by Philip Daniel Loewen and published by American Mathematical Soc.. This book was released on 1993 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Variational Analysis and Generalized Differentiation II written by Boris S. Mordukhovich and published by Springer Science & Business Media. This book was released on 2006-03-02 with total page 630 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive and state-of-the art study of the basic concepts and principles of variational analysis and generalized differentiation in both finite-dimensional and infinite-dimensional spaces Presents numerous applications to problems in the optimization, equilibria, stability and sensitivity, control theory, economics, mechanics, etc.
Download or read book Counterexamples in Optimal Control Theory written by S. I︠A︡ Serovaĭskiĭ and published by Walter de Gruyter. This book was released on 2004 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph deals with cases where optimal control either does not exist or is not unique, cases where optimality conditions are insufficient of degenerate, or where extremum problems in the sense of Tikhonov and Hadamard are ill-posed, and other situations. A formal application of classical optimisation methods in such cases either leads to wrong results or has no effect. The detailed analysis of these examples should provide a better understanding of the modern theory of optimal control and the practical difficulties of solving extremum problems.
Download or read book Variational and Optimal Control Problems on Unbounded Domains written by Gershon Wolansky and published by American Mathematical Soc.. This book was released on 2014-07-01 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the workshop on Variational and Optimal Control Problems on Unbounded Domains, held in memory of Arie Leizarowitz, from January 9-12, 2012, in Haifa, Israel. The workshop brought together a select group of worldwide experts in optimal control theory and the calculus of variations, working on problems on unbounded domains. The papers in this volume cover many different areas of optimal control and its applications. Topics include needle variations in infinite-horizon optimal control, Lyapunov stability with some extensions, small noise large time asymptotics for the normalized Feynman-Kac semigroup, linear-quadratic optimal control problems with state delays, time-optimal control of wafer stage positioning, second order optimality conditions in optimal control, state and time transformations of infinite horizon problems, turnpike properties of dynamic zero-sum games, and an infinite-horizon variational problem on an infinite strip. This book is co-published with Bar-Ilan University (Ramat-Gan, Israel).
Download or read book Optimal Control of Variational Inequalities written by Viorel Barbu and published by Pitman Advanced Publishing Program. This book was released on 1984 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt:
