Nonconvex Optimal Control And Variational Problems

Author : Alexander J. Zaslavski
Publisher : Springer Science & Business Media
Page : 382 pages
File Size : 44,5 Mb
Release : 2013-06-12
Category : Mathematics
ISBN : 9781461473787

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Nonconvex Optimal Control and Variational Problems by Alexander J. Zaslavski Pdf

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 : Pablo Pedregal
Publisher : SIAM
Page : 202 pages
File Size : 45,5 Mb
Release : 2022-07-26
Category : Mathematics
ISBN : 9781611977110

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A Variational Approach to Optimal Control of ODEs by Pablo Pedregal Pdf

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.

Author : Alexander Ioffe,Simeon Reich,I Shafrir
Publisher : CRC Press
Page : 278 pages
File Size : 45,6 Mb
Release : 2021-02-27
Category : Mathematics
ISBN : 9781000657401

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Calculus of Variations and Optimal Control by Alexander Ioffe,Simeon Reich,I Shafrir Pdf

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 : Philip Daniel Loewen
Publisher : American Mathematical Soc.
Page : 112 pages
File Size : 51,5 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.

Author : J Gregory
Publisher : CRC Press
Page : 232 pages
File Size : 53,7 Mb
Release : 2018-01-18
Category : Mathematics
ISBN : 9781351079310

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Constrained Optimization In The Calculus Of Variations and Optimal Control Theory by J Gregory Pdf

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.

Author : Alexander J. Zaslavski
Publisher : Springer Science & Business Media
Page : 396 pages
File Size : 44,6 Mb
Release : 2006-01-27
Category : Mathematics
ISBN : 9780387281544

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Turnpike Properties in the Calculus of Variations and Optimal Control by Alexander J. Zaslavski Pdf

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 : Zhongjing Ma,Suli Zou
Publisher : Springer
Page : 344 pages
File Size : 44,9 Mb
Release : 2022-02-14
Category : Technology & Engineering
ISBN : 9813362944

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Optimal Control Theory by Zhongjing Ma,Suli Zou Pdf

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 : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 55,6 Mb
Release : 2024-06-17
Category : Electronic
ISBN : 9789814475808

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Control Theory and Related Topics by Anonim Pdf

Author : Yeol Je Cho
Publisher : Nova Publishers
Page : 182 pages
File Size : 54,8 Mb
Release : 2007-07-02
Category : Mathematics
ISBN : 1594548781

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Differential Equations and Applications by Yeol Je Cho Pdf

Preface; Existence for set Differential Equations via Multivalued Operator Equations; Nonlocal Cauchy Problem for Abstract Functional Integrodifferential Equations; Existence Results for Discontinuous Functional Evolution Equations in Abstract Spaces; A Generalised Solution of the Black-Scholes Partial Differential Equation; Optimality and Duality for Multiobjective Fractional Programming with Generalised Invexity; Markovian Approach to the Backward Recurrence Time; A Multiplicity Result of Singular Boundary Value Problems for Second Order Impulsive Differential Equations; Extremal Solutions of Initial Value Problem for Non-linear Second Order Impulsive Integro-Differential Equations of Volterra Type in Banach Spaces; Construction of Upper and Lower Solutions for Singular p-Laplacian Equations with Sign Changing Nonlinearities; A Qualitative Hamiltonian Model for Human Motion; ; Newton's Method for Matrix Polynomials; Admissibility and Non-Uniform Dichotomy for Differential Systems; Boundary Value Problems of Fuzzy Differential Equations on an Infinite Interval; An Ultimate Boundedness Result for a Certain System of Fourth Order Non-linear Differential Equations; The Initial Value Problems for the First Order System of Non-linear Impulsive Integro-Differential Equations; Generic Well-Posedness of Nonconvex Optimal Control Problems; Index.

Author : Tomáš Roubíček
Publisher : Walter de Gruyter GmbH & Co KG
Page : 602 pages
File Size : 52,6 Mb
Release : 2020-11-09
Category : Mathematics
ISBN : 9783110590852

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Relaxation in Optimization Theory and Variational Calculus by Tomáš Roubíček Pdf

The relaxation method has enjoyed an intensive development during many decades and this new edition of this comprehensive text reflects in particular the main achievements in the past 20 years. Moreover, many further improvements and extensions are included, both in the direction of optimal control and optimal design as well as in numerics and applications in materials science, along with an updated treatment of the abstract parts of the theory.

Author : S. I︠A︡ Serovaĭskiĭ
Publisher : Walter de Gruyter
Page : 192 pages
File Size : 49,6 Mb
Release : 2004
Category : Mathematics
ISBN : 9067644005

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Counterexamples in Optimal Control Theory by S. I︠A︡ Serovaĭskiĭ Pdf

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.

Author : Viorel Barbu
Publisher : Pitman Advanced Publishing Program
Page : 316 pages
File Size : 48,7 Mb
Release : 1984
Category : Mathematics
ISBN : UCAL:B4405648

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Optimal Control of Variational Inequalities by Viorel Barbu Pdf

Author : Ivan Lirkov,Svetozar D. Margenov,Jerzy Wasniewski
Publisher : Springer
Page : 758 pages
File Size : 55,9 Mb
Release : 2009-03-26
Category : Computers
ISBN : 9783540788270

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Large-Scale Scientific Computing by Ivan Lirkov,Svetozar D. Margenov,Jerzy Wasniewski Pdf

Coverage in this proceedings volume includes robust multilevel and hierarchical preconditioning methods, applications for large scale computations and optimization of coupled engineering problems, and applications of metaheuristics to large-scale problems.

Author : F. Giannessi,A. Maugeri,Panos M. Pardalos
Publisher : Springer Science & Business Media
Page : 304 pages
File Size : 55,9 Mb
Release : 2006-04-11
Category : Mathematics
ISBN : 9780306480263

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Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models by F. Giannessi,A. Maugeri,Panos M. Pardalos Pdf

The aim of the book is to cover the three fundamental aspects of research in equilibrium problems: the statement problem and its formulation using mainly variational methods, its theoretical solution by means of classical and new variational tools, the calculus of solutions and applications in concrete cases. The book shows how many equilibrium problems follow a general law (the so-called user equilibrium condition). Such law allows us to express the problem in terms of variational inequalities. Variational inequalities provide a powerful methodology, by which existence and calculation of the solution can be obtained.

Author : Ivar Ekeland,Roger Temam
Publisher : SIAM
Page : 414 pages
File Size : 51,5 Mb
Release : 1999-12-01
Category : Mathematics
ISBN : 161197108X

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Convex Analysis and Variational Problems by Ivar Ekeland,Roger Temam Pdf

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.