Applied and Computational Optimal Control

Applied and Computational Optimal Control
Author: Kok Lay Teo
Publisher: Springer Nature
Total Pages: 581
Release: 2021-05-24
Genre: Mathematics
ISBN: 3030699137
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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.

A Unified Computational Approach to Optimal Control Problems

A Unified Computational Approach to Optimal Control Problems
Author: K. L. Teo
Publisher:
Total Pages: 360
Release: 1991
Genre: Mathematics
ISBN:
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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.

Computational Methods in Optimal Control Problems

Computational Methods in Optimal Control Problems
Author: I.H. Mufti
Publisher: Springer Science & Business Media
Total Pages: 54
Release: 2012-12-06
Genre: Mathematics
ISBN: 3642859607
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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.

Computational Optimal Control

Computational Optimal Control
Author: Dr Subchan Subchan
Publisher: John Wiley & Sons
Total Pages: 202
Release: 2009-08-19
Genre: Technology & Engineering
ISBN: 0470747684
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Computational Optimal Control: Tools and Practice provides a detailed guide to informed use of computational optimal control in advanced engineering practice, addressing the need for a better understanding of the practical application of optimal control using computational techniques. Throughout the text the authors employ an advanced aeronautical case study to provide a practical, real-life setting for optimal control theory. This case study focuses on an advanced, real-world problem known as the “terminal bunt manoeuvre” or special trajectory shaping of a cruise missile. Representing the many problems involved in flight dynamics, practical control and flight path constraints, this case study offers an excellent illustration of advanced engineering practice using optimal solutions. The book describes in practical detail the real and tested optimal control software, examining the advantages and limitations of the technology. Featuring tutorial insights into computational optimal formulations and an advanced case-study approach to the topic, Computational Optimal Control: Tools and Practice provides an essential handbook for practising engineers and academics interested in practical optimal solutions in engineering. Focuses on an advanced, real-world aeronautical case study examining optimisation of the bunt manoeuvre Covers DIRCOL, NUDOCCCS, PROMIS and SOCS (under the GESOP environment), and BNDSCO Explains how to configure and optimize software to solve complex real-world computational optimal control problems Presents a tutorial three-stage hybrid approach to solving optimal control problem formulations

A Relaxation-Based Approach to Optimal Control of Hybrid and Switched Systems

A Relaxation-Based Approach to Optimal Control of Hybrid and Switched Systems
Author: Vadim Azhmyakov
Publisher: Butterworth-Heinemann
Total Pages: 434
Release: 2019-02-14
Genre: Mathematics
ISBN: 012814789X
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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

Computational Methods for Optimal Design and Control

Computational Methods for Optimal Design and Control
Author: J. Borggaard
Publisher: Springer Science & Business Media
Total Pages: 467
Release: 2012-12-06
Genre: Technology & Engineering
ISBN: 1461217806
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This volume contains the proceedings of the Second International Workshop on Optimal Design and Control, held in Arlington, Virginia, 30 September-3 Octo ber, 1997. The First Workshop was held in Blacksburg, Virginia in 1994. The proceedings of that meeting also appeared in the Birkhauser series on Progress in Systems and Control Theory and may be obtained through Birkhauser. These workshops were sponsored by the Air Force Office of Scientific Re search through the Center for Optimal Design and Control (CODAC) at Vrrginia Tech. The meetings provided a forum for the exchange of new ideas and were designed to bring together diverse viewpoints and to highlight new applications. The primary goal of the workshops was to assess the current status of research and to analyze future directions in optimization based design and control. The present volume contains the technical papers presented at the Second Workshop. More than 65 participants from 6 countries attended the meeting and contributed to its success. It has long been recognized that many modern optimal design problems are best viewed as variational and optimal control problems. Indeed, the famous problem of determining the body of revolution that produces a minimum drag nose shape in hypersonic How was first proposed by Newton in 1686. Optimal control approaches to design can provide theoretical and computational insight into these problems. This volume contains a number of papers which deal with computational aspects of optimal control.