Nonconvex Optimal Control And Variational Problems PDF Download
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| Author | : Alexander J. Zaslavski |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 382 |
| Release | : 2013-06-12 |
| Genre | : Mathematics |
| ISBN | : 1461473780 |
Download Nonconvex Optimal Control and Variational Problems Book in PDF, ePub and Kindle
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.
| Author | : Alexander Ioffe |
| Publisher | : CRC Press |
| Total Pages | : 278 |
| Release | : 2021-02-27 |
| Genre | : Mathematics |
| ISBN | : 100065740X |
Download Calculus of Variations and Optimal Control Book in PDF, ePub and Kindle
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.
| Author | : Alexander J. Zaslavski |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 407 |
| Release | : 2006-01-27 |
| Genre | : Mathematics |
| ISBN | : 0387281541 |
Download Turnpike Properties in the Calculus of Variations and Optimal Control Book in PDF, ePub and Kindle
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.
| Author | : Vadim Krotov |
| Publisher | : CRC Press |
| Total Pages | : 410 |
| Release | : 1995-10-13 |
| Genre | : Mathematics |
| ISBN | : 9780824793296 |
Download Global Methods in Optimal Control Theory Book in PDF, ePub and Kindle
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.
| Author | : Ivar Ekeland |
| Publisher | : SIAM |
| Total Pages | : 414 |
| Release | : 1999-12-01 |
| Genre | : Mathematics |
| ISBN | : 9781611971088 |
Download Convex Analysis and Variational Problems Book in PDF, ePub and Kindle
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.
| Author | : Altannar Chinchuluun |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 508 |
| Release | : 2010-07-07 |
| Genre | : Mathematics |
| ISBN | : 0387894950 |
Download Optimization and Optimal Control Book in PDF, ePub and Kindle
Optimization and optimal control are the main tools in decision making. Because of their numerous applications in various disciplines, research in these areas is accelerating at a rapid pace. “Optimization and Optimal Control: Theory and Applications” brings together the latest developments in these areas of research as well as presents applications of these results to a wide range of real-world problems. This volume can serve as a useful resource for researchers, practitioners, and advanced graduate students of mathematics and engineering working in research areas where results in optimization and optimal control can be applied.
| Author | : Zhongjing Ma |
| Publisher | : Springer Nature |
| Total Pages | : 355 |
| Release | : 2021-01-30 |
| Genre | : Technology & Engineering |
| ISBN | : 9813362928 |
Download Optimal Control Theory Book in PDF, ePub and Kindle
This book focuses on how to implement optimal control problems via the variational method. It studies how to implement the extrema of functional by applying the variational method and covers the extrema of functional with different boundary conditions, involving multiple functions and with certain constraints etc. It gives the necessary and sufficient condition for the (continuous-time) optimal control solution via the variational method, solves the optimal control problems with different boundary conditions, analyzes the linear quadratic regulator & tracking problems respectively in detail, and provides the solution of optimal control problems with state constraints by applying the Pontryagin’s minimum principle which is developed based upon the calculus of variations. And the developed results are applied to implement several classes of popular optimal control problems and say minimum-time, minimum-fuel and minimum-energy problems and so on. As another key branch of optimal control methods, it also presents how to solve the optimal control problems via dynamic programming and discusses the relationship between the variational method and dynamic programming for comparison. Concerning the system involving individual agents, it is also worth to study how to implement the decentralized solution for the underlying optimal control problems in the framework of differential games. The equilibrium is implemented by applying both Pontryagin’s minimum principle and dynamic programming. The book also analyzes the discrete-time version for all the above materials as well since the discrete-time optimal control problems are very popular in many fields.
| Author | : Philip Daniel Loewen |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 112 |
| Release | : 1993 |
| Genre | : Control theory |
| ISBN | : 9780821869963 |
Download Optimal Control Via Nonsmooth Analysis Book in PDF, ePub and Kindle
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.
| Author | : R. Tyrrell Rockafellar |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 747 |
| Release | : 2009-06-26 |
| Genre | : Mathematics |
| ISBN | : 3642024319 |
Download Variational Analysis Book in PDF, ePub and Kindle
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.
| Author | : Boris S. Mordukhovich |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 630 |
| Release | : 2006-03-02 |
| Genre | : Mathematics |
| ISBN | : 3540312463 |
Download Variational Analysis and Generalized Differentiation II Book in PDF, ePub and Kindle
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.
