Download or read book A Primer on Pontryagin s Principle in Optimal Control written by I. Michael Ross and published by . This book was released on 2009 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces a student to Pontryagin's "Maximum" Principle in a tutorial style. How to formulate an optimal control problem and how to apply Pontryagin's theory are the main topics. Numerous examples are used to discuss pitfalls in problem formulation. Figures are used extensively to complement the ideas. An entire chapter is dedicated to solved example problems: from the classical Brachistochrone problem to modern space vehicle guidance. These examples are also used to show how to obtain optimal nonlinear feedback control. Students in engineering and mathematics will find this book to be a useful complement to their lecture notes. Table of Contents: 1 Problem Formulation 1.1 The Brachistochrone Paradigm 1.1.1 Development of a Problem Formulation 1.1.2 Scaling Equations 1.1.3 Alternative Problem Formulations 1.1.4 The Target Set 1.2 A Fundamental Control Problem 1.2.1 Problem Statement 1.2.2 Trajectory Optimization and Feedback Control 2 Pontryagin's Principle 2.1 A Fundamental Control Problem 2.2 Necessary Conditions 2.3 Minimizing the Hamiltonian 2.3.1 Brief History 2.3.2 KKT Conditions for Problem HMC 2.3.3 Time-Varying Control Space 3 Example Problems 3.1 The Brachistochrone Problem Redux 3.2 A Linear-Quadratic Problem 3.3 A Time-Optimal Control Problem 3.4 A Space Guidance Problem 4 Exercise Problems 4.1 One-Dimensional Problems 4.1.1 Linear-Quadratic Problems 4.1.2 A Control-Constrained Problem 4.2 Double Integrator Problems 4.2.1 L1-Optimal Control 4.2.2 Fuller's Problem 4.3 Orbital Maneuvering Problems 4.3.1 Velocity Steering 4.3.2 Max-Energy Orbit Transfer 4.3.3 Min-Time Orbit Transfer References Index

Download or read book Primer on Optimal Control Theory written by Jason L. Speyer and published by SIAM. This book was released on 2010-01-01 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: The performance of a process -- for example, how an aircraft consumes fuel -- can be enhanced when the most effective controls and operating points for the process are determined. This holds true for many physical, economic, biomedical, manufacturing, and engineering processes whose behavior can often be influenced by altering certain parameters or controls to optimize some desired property or output.

Download or read book Optimal Control of a Double Integrator written by Arturo Locatelli and published by Springer. This book was released on 2016-07-26 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introductory yet rigorous treatment of Pontryagin’s Maximum Principle and its application to optimal control problems when simple and complex constraints act on state and control variables, the two classes of variable in such problems. The achievements resulting from first-order variational methods are illustrated with reference to a large number of problems that, almost universally, relate to a particular second-order, linear and time-invariant dynamical system, referred to as the double integrator. The book is ideal for students who have some knowledge of the basics of system and control theory and possess the calculus background typically taught in undergraduate curricula in engineering. Optimal control theory, of which the Maximum Principle must be considered a cornerstone, has been very popular ever since the late 1950s. However, the possibly excessive initial enthusiasm engendered by its perceived capability to solve any kind of problem gave way to its equally unjustified rejection when it came to be considered as a purely abstract concept with no real utility. In recent years it has been recognized that the truth lies somewhere between these two extremes, and optimal control has found its (appropriate yet limited) place within any curriculum in which system and control theory plays a significant role.

Download or read book A Primer on the Calculus of Variations and Optimal Control Theory written by Mike Mesterton-Gibbons and published by American Mathematical Soc.. This book was released on 2009 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: The calculus of variations is used to find functions that optimize quantities expressed in terms of integrals. Optimal control theory seeks to find functions that minimize cost integrals for systems described by differential equations. This book is an introduction to both the classical theory of the calculus of variations and the more modern developments of optimal control theory from the perspective of an applied mathematician. It focuses on understanding concepts and how to apply them. The range of potential applications is broad: the calculus of variations and optimal control theory have been widely used in numerous ways in biology, criminology, economics, engineering, finance, management science, and physics. Applications described in this book include cancer chemotherapy, navigational control, and renewable resource harvesting. The prerequisites for the book are modest: the standard calculus sequence, a first course on ordinary differential equations, and some facility with the use of mathematical software. It is suitable for an undergraduate or beginning graduate course, or for self study. It provides excellent preparation for more advanced books and courses on the calculus of variations and optimal control theory.

Download or read book Calculus of Variations and Optimal Control Theory written by Daniel Liberzon and published by Princeton University Press. This book was released on 2012 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook offers a concise yet rigorous introduction to calculus of variations and optimal control theory, and is a self-contained resource for graduate students in engineering, applied mathematics, and related subjects. Designed specifically for a one-semester course, the book begins with calculus of variations, preparing the ground for optimal control. It then gives a complete proof of the maximum principle and covers key topics such as the Hamilton-Jacobi-Bellman theory of dynamic programming and linear-quadratic optimal control. Calculus of Variations and Optimal Control Theory also traces the historical development of the subject and features numerous exercises, notes and references at the end of each chapter, and suggestions for further study. Offers a concise yet rigorous introduction Requires limited background in control theory or advanced mathematics Provides a complete proof of the maximum principle Uses consistent notation in the exposition of classical and modern topics Traces the historical development of the subject Solutions manual (available only to teachers) Leading universities that have adopted this book include: University of Illinois at Urbana-Champaign ECE 553: Optimum Control Systems Georgia Institute of Technology ECE 6553: Optimal Control and Optimization University of Pennsylvania ESE 680: Optimal Control Theory University of Notre Dame EE 60565: Optimal Control

Download or read book Optimal Control Theory written by Donald E. Kirk and published by Courier Corporation. This book was released on 2012-04-26 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: Upper-level undergraduate text introduces aspects of optimal control theory: dynamic programming, Pontryagin's minimum principle, and numerical techniques for trajectory optimization. Numerous figures, tables. Solution guide available upon request. 1970 edition.

Download or read book Introduction to Optimal Control Theory written by Jack Macki and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is an introduction to optimal control theory for systems governed by vector ordinary differential equations. It is not intended as a state-of-the-art handbook for researchers. We have tried to keep two types of reader in mind: (1) mathematicians, graduate students, and advanced undergraduates in mathematics who want a concise introduction to a field which contains nontrivial interesting applications of mathematics (for example, weak convergence, convexity, and the theory of ordinary differential equations); (2) economists, applied scientists, and engineers who want to understand some of the mathematical foundations. of optimal control theory. In general, we have emphasized motivation and explanation, avoiding the "definition-axiom-theorem-proof" approach. We make use of a large number of examples, especially one simple canonical example which we carry through the entire book. In proving theorems, we often just prove the simplest case, then state the more general results which can be proved. Many of the more difficult topics are discussed in the "Notes" sections at the end of chapters and several major proofs are in the Appendices. We feel that a solid understanding of basic facts is best attained by at first avoiding excessive generality. We have not tried to give an exhaustive list of references, preferring to refer the reader to existing books or papers with extensive bibliographies. References are given by author's name and the year of publication, e.g., Waltman [1974].

Download or read book Optimal Control with Engineering Applications written by Hans P. Geering and published by Springer Science & Business Media. This book was released on 2007-03-23 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces a variety of problem statements in classical optimal control, in optimal estimation and filtering, and in optimal control problems with non-scalar-valued performance criteria. Many example problems are solved completely in the body of the text. All chapter-end exercises are sketched in the appendix. The theoretical part of the book is based on the calculus of variations, so the exposition is very transparent and requires little mathematical rigor.

Download or read book Optimal Control with Aerospace Applications written by James M Longuski and published by Springer Science & Business Media. This book was released on 2013-11-04 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: Want to know not just what makes rockets go up but how to do it optimally? Optimal control theory has become such an important field in aerospace engineering that no graduate student or practicing engineer can afford to be without a working knowledge of it. This is the first book that begins from scratch to teach the reader the basic principles of the calculus of variations, develop the necessary conditions step-by-step, and introduce the elementary computational techniques of optimal control. This book, with problems and an online solution manual, provides the graduate-level reader with enough introductory knowledge so that he or she can not only read the literature and study the next level textbook but can also apply the theory to find optimal solutions in practice. No more is needed than the usual background of an undergraduate engineering, science, or mathematics program: namely calculus, differential equations, and numerical integration. Although finding optimal solutions for these problems is a complex process involving the calculus of variations, the authors carefully lay out step-by-step the most important theorems and concepts. Numerous examples are worked to demonstrate how to apply the theories to everything from classical problems (e.g., crossing a river in minimum time) to engineering problems (e.g., minimum-fuel launch of a satellite). Throughout the book use is made of the time-optimal launch of a satellite into orbit as an important case study with detailed analysis of two examples: launch from the Moon and launch from Earth. For launching into the field of optimal solutions, look no further!

Download or read book Introduction to Control Theory Including Optimal Control written by David N. Burghes and published by . This book was released on 1980 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Optimal Control written by Leslie M. Hocking and published by Oxford University Press. This book was released on 1991 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: Systems that evolve with time occur frequently in nature and modelling the behavior of such systems provides an important application of mathematics. These systems can be completely deterministic, but it may be possible too to control their behavior by intervention through "controls". The theory of optimal control is concerned with determining such controls which, at minimum cost, either direct the system along a given trajectory or enable it to reach a given point in its state space. This textbook is a straightforward introduction to the theory of optimal control with an emphasis on presenting many different applications. Professor Hocking has taken pains to ensure that the theory is developed to display the main themes of the arguments but without using sophisticated mathematical tools. Problems in this setting can arise across a wide range of subjects and there are illustrative examples of systems from fields as diverse as dynamics, economics, population control, and medicine. Throughout there are many worked examples, and numerous exercises (with solutions) are provided.

Download or read book Classical Mechanics with Calculus of Variations and Optimal Control written by Mark Levi and published by American Mathematical Soc.. This book was released on 2014-03-07 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an intuitively motivated presentation of many topics in classical mechanics and related areas of control theory and calculus of variations. All topics throughout the book are treated with zero tolerance for unrevealing definitions and for proofs which leave the reader in the dark. Some areas of particular interest are: an extremely short derivation of the ellipticity of planetary orbits; a statement and an explanation of the "tennis racket paradox"; a heuristic explanation (and a rigorous treatment) of the gyroscopic effect; a revealing equivalence between the dynamics of a particle and statics of a spring; a short geometrical explanation of Pontryagin's Maximum Principle, and more. In the last chapter, aimed at more advanced readers, the Hamiltonian and the momentum are compared to forces in a certain static problem. This gives a palpable physical meaning to some seemingly abstract concepts and theorems. With minimal prerequisites consisting of basic calculus and basic undergraduate physics, this book is suitable for courses from an undergraduate to a beginning graduate level, and for a mixed audience of mathematics, physics and engineering students. Much of the enjoyment of the subject lies in solving almost 200 problems in this book.

Download or read book An Introduction to Optimal Control Theory written by Aaron Strauss and published by . This book was released on 1968 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This paper is intended for the beginner. It is not a state-of-the-art paper for research workers in the field of control theory. Its purpose is to introduce the reader to some of the problems and results in control theory, to illustrate the application of these results, and to provide a guide for his further reading on this subject."--Preface.

Download or read book Optimal Control Systems written by D. Subbaram Naidu and published by CRC Press. This book was released on 2018-10-03 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of optimal control systems has grown and flourished since the 1960's. Many texts, written on varying levels of sophistication, have been published on the subject. Yet even those purportedly designed for beginners in the field are often riddled with complex theorems, and many treatments fail to include topics that are essential to a thorough grounding in the various aspects of and approaches to optimal control. Optimal Control Systems provides a comprehensive but accessible treatment of the subject with just the right degree of mathematical rigor to be complete but practical. It provides a solid bridge between "traditional" optimization using the calculus of variations and what is called "modern" optimal control. It also treats both continuous-time and discrete-time optimal control systems, giving students a firm grasp on both methods. Among this book's most outstanding features is a summary table that accompanies each topic or problem and includes a statement of the problem with a step-by-step solution. Students will also gain valuable experience in using industry-standard MATLAB and SIMULINK software, including the Control System and Symbolic Math Toolboxes. Diverse applications across fields from power engineering to medicine make a foundation in optimal control systems an essential part of an engineer's background. This clear, streamlined presentation is ideal for a graduate level course on control systems and as a quick reference for working engineers.

Download or read book Energy Efficient Train Control written by Philip G. Howlett and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rail is potentially a very efficient form of transport, but must be convenient, reliable and cost-effective to compete with road and air transport. Optimal control can be used to find energy-efficient driving strategies for trains. This book describes the train control problem and shows how a solution was found at the University of South Australia. This research was used to develop the Metromiser system, which provides energy-efficient driving advice on suburban trains. Since then, this work has been modified to find practical driving strategies for long-haul trains. The authors describe the history of the problem, reviewing the basic mathematical analysis and relevant techniques of constrained optimisation. They outline the modelling and solution of the problem and finally explain how the fuel consumption can be minimised for a journey, showing the effect of speed limits and track gradients on the optimal driving strategy.

Download or read book Geometry of Submanifolds and Homogeneous Spaces written by Andreas Arvanitoyeorgos and published by MDPI. This book was released on 2020-01-03 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present Special Issue of Symmetry is devoted to two important areas of global Riemannian geometry, namely submanifold theory and the geometry of Lie groups and homogeneous spaces. Submanifold theory originated from the classical geometry of curves and surfaces. Homogeneous spaces are manifolds that admit a transitive Lie group action, historically related to F. Klein's Erlangen Program and S. Lie's idea to use continuous symmetries in studying differential equations. In this Special Issue, we provide a collection of papers that not only reflect some of the latest advancements in both areas, but also highlight relations between them and the use of common techniques. Applications to other areas of mathematics are also considered.

Download or read book Primer on Optimal Control Theory written by Jason L. Speyer and published by SIAM. This book was released on 2010-05-13 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: A rigorous introduction to optimal control theory, which will enable engineers and scientists to put the theory into practice.