A Unified Computational Approach To Optimal Control Problems
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A Unified Computational Approach To Optimal Control Problems
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Author : K. L. Teo
language : en
Publisher:
Release Date : 1991
A Unified Computational Approach To Optimal Control Problems written by K. L. Teo and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with categories.
A Unified Computational Approach To Optimal Control Problems
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Author : K. L. Teo
language : en
Publisher: Longman Sc & Tech
Release Date : 1991
A Unified Computational Approach To Optimal Control Problems written by K. L. Teo and has been published by Longman Sc & Tech this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Technology & Engineering categories.
Applied And Computational Optimal Control
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Author : Kok Lay Teo
language : en
Publisher: Springer Nature
Release Date : 2021-05-24
Applied And Computational Optimal Control written by Kok Lay Teo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-24 with Mathematics categories.
The aim of this book is to furnish the reader with a rigorous and detailed exposition of the concept of control parametrization and time scaling transformation. It presents computational solution techniques for a special class of constrained optimal control problems as well as applications to some practical examples. The book may be considered an extension of the 1991 monograph A Unified Computational Approach Optimal Control Problems, by K.L. Teo, C.J. Goh, and K.H. Wong. This publication discusses the development of new theory and computational methods for solving various optimal control problems numerically and in a unified fashion. To keep the book accessible and uniform, it includes those results developed by the authors, their students, and their past and present collaborators. A brief review of methods that are not covered in this exposition, is also included. Knowledge gained from this book may inspire advancement of new techniques to solve complex problems that arise in the future. This book is intended as reference for researchers in mathematics, engineering, and other sciences, graduate students and practitioners who apply optimal control methods in their work. It may be appropriate reading material for a graduate level seminar or as a text for a course in optimal control.
Computational Methods In Optimal Control Problems
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Author : I.H. Mufti
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Computational Methods In Optimal Control Problems written by I.H. Mufti and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The purpose of this modest report is to present in a simplified manner some of the computational methods that have been developed in the last ten years for the solution of optimal control problems. Only those methods that are based on the minimum (maximum) principle of Pontriagin are discussed here. The autline of the report is as follows: In the first two sections a control problem of Bolza is formulated and the necessary conditions in the form of the minimum principle are given. The method of steepest descent and a conjugate gradient-method are dis cussed in Section 3. In the remaining sections, the successive sweep method, the Newton-Raphson method and the generalized Newton-Raphson method (also called quasilinearization method) ar~ presented from a unified approach which is based on the application of Newton Raphson approximation to the necessary conditions of optimality. The second-variation method and other shooting methods based on minimizing an error function are also considered. TABLE OF CONTENTS 1. 0 INTRODUCTION 1 2. 0 NECESSARY CONDITIONS FOR OPTIMALITY •••••••• 2 3. 0 THE GRADIENT METHOD 4 3. 1 Min H Method and Conjugate Gradient Method •. •••••••••. . . . ••••••. ••••••••. • 8 3. 2 Boundary Constraints •••••••••••. ••••. • 9 3. 3 Problems with Control Constraints ••. •• 15 4. 0 SUCCESSIVE SWEEP METHOD •••••••••••••••••••• 18 4. 1 Final Time Given Implicitly ••••. •••••• 22 5. 0 SECOND-VARIATION METHOD •••••••••••••••••••• 23 6. 0 SHOOTING METHODS ••••••••••••••••••••••••••• 27 6. 1 Newton-Raphson Method ••••••••••••••••• 27 6.
A Variational Approach To Optimal Control Of Odes
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Author : Pablo Pedregal
language : en
Publisher: SIAM
Release Date : 2022-07-26
A Variational Approach To Optimal Control Of Odes written by Pablo Pedregal and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-26 with Mathematics categories.
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.
A Unified Computational Approach To Optimal Control Problems
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Author : K. L. Teo
language : en
Publisher:
Release Date : 1991
A Unified Computational Approach To Optimal Control Problems written by K. L. Teo and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.
Concerned with optimal control theory, this text aims to supplement existing work in this field from the viewpoints of computation and applications. In particular those computational algorithms derived from the concept of control parametrization are emphasized in this text.
A Relaxation Based Approach To Optimal Control Of Hybrid And Switched Systems
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Author : Vadim Azhmyakov
language : en
Publisher: Butterworth-Heinemann
Release Date : 2019-02-14
A Relaxation Based Approach To Optimal Control Of Hybrid And Switched Systems written by Vadim Azhmyakov and has been published by Butterworth-Heinemann this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-14 with Mathematics categories.
A Relaxation Based Approach to Optimal Control of Hybrid and Switched Systems proposes a unified approach to effective and numerically tractable relaxation schemes for optimal control problems of hybrid and switched systems. The book gives an overview of the existing (conventional and newly developed) relaxation techniques associated with the conventional systems described by ordinary differential equations. Next, it constructs a self-contained relaxation theory for optimal control processes governed by various types (sub-classes) of general hybrid and switched systems. It contains all mathematical tools necessary for an adequate understanding and using of the sophisticated relaxation techniques. In addition, readers will find many practically oriented optimal control problems related to the new class of dynamic systems. All in all, the book follows engineering and numerical concepts. However, it can also be considered as a mathematical compendium that contains the necessary formal results and important algorithms related to the modern relaxation theory. Illustrates the use of the relaxation approaches in engineering optimization Presents application of the relaxation methods in computational schemes for a numerical treatment of the sophisticated hybrid/switched optimal control problems Offers a rigorous and self-contained mathematical tool for an adequate understanding and practical use of the relaxation techniques Presents an extension of the relaxation methodology to the new class of applied dynamic systems, namely, to hybrid and switched control systems
Optimal Control Novel Directions And Applications
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Author : Daniela Tonon
language : en
Publisher: Springer
Release Date : 2017-09-01
Optimal Control Novel Directions And Applications written by Daniela Tonon and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-01 with Mathematics categories.
Focusing on applications to science and engineering, this book presents the results of the ITN-FP7 SADCO network’s innovative research in optimization and control in the following interconnected topics: optimality conditions in optimal control, dynamic programming approaches to optimal feedback synthesis and reachability analysis, and computational developments in model predictive control. The novelty of the book resides in the fact that it has been developed by early career researchers, providing a good balance between clarity and scientific rigor. Each chapter features an introduction addressed to PhD students and some original contributions aimed at specialist researchers. Requiring only a graduate mathematical background, the book is self-contained. It will be of particular interest to graduate and advanced undergraduate students, industrial practitioners and to senior scientists wishing to update their knowledge.
Nonlinear And Optimal Control Systems
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Author : Thomas L. Vincent
language : en
Publisher: John Wiley & Sons
Release Date : 1997-06-23
Nonlinear And Optimal Control Systems written by Thomas L. Vincent and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-06-23 with Science categories.
Designed for one-semester introductory senior-or graduate-level course, the authors provide the student with an introduction of analysis techniques used in the design of nonlinear and optimal feedback control systems. There is special emphasis on the fundamental topics of stability, controllability, and optimality, and on the corresponding geometry associated with these topics. Each chapter contains several examples and a variety of exercises.
Optimal Control Of Drug Administration In Cancer Chemotherapy
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Author : Rory Martin
language : en
Publisher: World Scientific
Release Date : 1994
Optimal Control Of Drug Administration In Cancer Chemotherapy written by Rory Martin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Medical categories.
This monograph is a study of optimal control applied to cancer chemotherapy, the treatment of cancer using drugs that kill cancer cells. The aim is to determine whether current methods for the administration of chemotherapy are optimal, and if alternative regimens should be considered.The research utilizes the mathematical theory of optimal control, an active research area for many mathematicians, scientists, and engineers. It is of multidisciplinary nature, having been applied to areas ranging from engineering to biomedicine. The aim in optimal control is to achieve a given objective at minimum cost. A set of differential equations is used to describe the evolution in time of the process being modelled, and constraints limit the policies that can be used to attain the objective.In this monograph, mathematical models are used to construct optimal drug schedules. These are treatment guidelines specifying which drug to deliver, when, and at what dose. Many current drug schedules have been derived empirically, based upon ?rules of thumb?.The monograph has been structured so that most of the high-level mathematics is introduced in a special appendix. In this way, a scientist can skip the more subtle aspects of the theory and still understand the biomedical applications that follow. However, the text is self-contained so that a deeper understanding of the mathematics of optimal control can be gained from the mathematical appendix.The mathematical models in this book and the associated computer simulations show that low intensity chemotherapy is a better choice of treatment than high intensity chemotherapy, under certain conditions.