Optimal Control Of A Double Integrator

Author : Arturo Locatelli
Publisher : Springer
Page : 311 pages
File Size : 48,5 Mb
Release : 2016-07-26
Category : Technology & Engineering
ISBN : 9783319421261

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Optimal Control of a Double Integrator by Arturo Locatelli Pdf

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.

Author : Heinz Schättler,Urszula Ledzewicz
Publisher : Springer Science & Business Media
Page : 652 pages
File Size : 55,5 Mb
Release : 2012-06-26
Category : Mathematics
ISBN : 9781461438342

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Geometric Optimal Control by Heinz Schättler,Urszula Ledzewicz Pdf

This book gives a comprehensive treatment of the fundamental necessary and sufficient conditions for optimality for finite-dimensional, deterministic, optimal control problems. The emphasis is on the geometric aspects of the theory and on illustrating how these methods can be used to solve optimal control problems. It provides tools and techniques that go well beyond standard procedures and can be used to obtain a full understanding of the global structure of solutions for the underlying problem. The text includes a large number and variety of fully worked out examples that range from the classical problem of minimum surfaces of revolution to cancer treatment for novel therapy approaches. All these examples, in one way or the other, illustrate the power of geometric techniques and methods. The versatile text contains material on different levels ranging from the introductory and elementary to the advanced. Parts of the text can be viewed as a comprehensive textbook for both advanced undergraduate and all level graduate courses on optimal control in both mathematics and engineering departments. The text moves smoothly from the more introductory topics to those parts that are in a monograph style were advanced topics are presented. While the presentation is mathematically rigorous, it is carried out in a tutorial style that makes the text accessible to a wide audience of researchers and students from various fields, including the mathematical sciences and engineering. Heinz Schättler is an Associate Professor at Washington University in St. Louis in the Department of Electrical and Systems Engineering, Urszula Ledzewicz is a Distinguished Research Professor at Southern Illinois University Edwardsville in the Department of Mathematics and Statistics.

Author : Eugene P. Ryan
Publisher : Institution of Electrical Engineers
Page : 360 pages
File Size : 45,8 Mb
Release : 1982
Category : Technology & Engineering
ISBN : STANFORD:36105030359108

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Optimal Relay and Saturating Control System Synthesis by Eugene P. Ryan Pdf

Author : Daniel Liberzon
Publisher : Princeton University Press
Page : 255 pages
File Size : 54,8 Mb
Release : 2012
Category : Mathematics
ISBN : 9780691151878

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Calculus of Variations and Optimal Control Theory by Daniel Liberzon Pdf

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

Author : Stephen J. Dodds
Publisher : Springer
Page : 1012 pages
File Size : 55,8 Mb
Release : 2015-07-18
Category : Technology & Engineering
ISBN : 9781447166757

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Feedback Control by Stephen J. Dodds Pdf

This book develops the understanding and skills needed to be able to tackle original control problems. The general approach to a given control problem is to try the simplest tentative solution first and, when this is insufficient, to explain why and use a more sophisticated alternative to remedy the deficiency and achieve satisfactory performance. This pattern of working gives readers a full understanding of different controllers and teaches them to make an informed choice between traditional controllers and more advanced modern alternatives in meeting the needs of a particular plant. Attention is focused on the time domain, covering model-based linear and nonlinear forms of control together with robust control based on sliding modes and the use of state observers such as disturbance estimation. Feedback Control is self-contained, paying much attention to explanations of underlying concepts, with detailed mathematical derivations being employed where necessary. Ample use is made of diagrams to aid these conceptual explanations and the subject matter is enlivened by continual use of examples and problems derived from real control applications. Readers’ learning is further enhanced by experimenting with the fully-commented MATLAB®/Simulink® simulation environment made accessible at insert URL here to produce simulations relevant to all of the topics covered in the text. A solutions manual for use by instructors adopting the book can also be downloaded from insert URL here. Feedback Control is suitable as a main textbook for graduate and final-year undergraduate courses containing control modules; knowledge of ordinary linear differential equations, Laplace transforms, transfer functions, poles and zeros, root locus and elementary frequency response analysis, and elementary feedback control is required. It is also a useful reference source on control design methods for engineers practicing in industry and for academic control researchers.

Author : Donald E. Kirk
Publisher : Courier Corporation
Page : 466 pages
File Size : 54,7 Mb
Release : 2012-04-26
Category : Technology & Engineering
ISBN : 9780486135076

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Optimal Control Theory by Donald E. Kirk Pdf

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.

Author : Lucian Busoniu,Robert Babuska,Bart De Schutter,Damien Ernst
Publisher : CRC Press
Page : 280 pages
File Size : 46,8 Mb
Release : 2017-07-28
Category : Computers
ISBN : 9781439821091

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Reinforcement Learning and Dynamic Programming Using Function Approximators by Lucian Busoniu,Robert Babuska,Bart De Schutter,Damien Ernst Pdf

From household appliances to applications in robotics, engineered systems involving complex dynamics can only be as effective as the algorithms that control them. While Dynamic Programming (DP) has provided researchers with a way to optimally solve decision and control problems involving complex dynamic systems, its practical value was limited by algorithms that lacked the capacity to scale up to realistic problems. However, in recent years, dramatic developments in Reinforcement Learning (RL), the model-free counterpart of DP, changed our understanding of what is possible. Those developments led to the creation of reliable methods that can be applied even when a mathematical model of the system is unavailable, allowing researchers to solve challenging control problems in engineering, as well as in a variety of other disciplines, including economics, medicine, and artificial intelligence. Reinforcement Learning and Dynamic Programming Using Function Approximators provides a comprehensive and unparalleled exploration of the field of RL and DP. With a focus on continuous-variable problems, this seminal text details essential developments that have substantially altered the field over the past decade. In its pages, pioneering experts provide a concise introduction to classical RL and DP, followed by an extensive presentation of the state-of-the-art and novel methods in RL and DP with approximation. Combining algorithm development with theoretical guarantees, they elaborate on their work with illustrative examples and insightful comparisons. Three individual chapters are dedicated to representative algorithms from each of the major classes of techniques: value iteration, policy iteration, and policy search. The features and performance of these algorithms are highlighted in extensive experimental studies on a range of control applications. The recent development of applications involving complex systems has led to a surge of interest in RL and DP methods and the subsequent need for a quality resource on the subject. For graduate students and others new to the field, this book offers a thorough introduction to both the basics and emerging methods. And for those researchers and practitioners working in the fields of optimal and adaptive control, machine learning, artificial intelligence, and operations research, this resource offers a combination of practical algorithms, theoretical analysis, and comprehensive examples that they will be able to adapt and apply to their own work. Access the authors' website at www.dcsc.tudelft.nl/rlbook/ for additional material, including computer code used in the studies and information concerning new developments.

Author : Rush D. Robinett III,David G. Wilson,G. Richard Eisler,John E. Hurtado
Publisher : SIAM
Page : 273 pages
File Size : 50,5 Mb
Release : 2005-07-01
Category : Mathematics
ISBN : 9780898715866

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Applied Dynamic Programming for Optimization of Dynamical Systems by Rush D. Robinett III,David G. Wilson,G. Richard Eisler,John E. Hurtado Pdf

This book presents a range of dynamic programming (DP) techniques applied to the optimization of dynamical systems.

Author : Abdullah Al Mamun,GuoXiao Guo,Chao Bi
Publisher : CRC Press
Page : 359 pages
File Size : 54,9 Mb
Release : 2017-12-19
Category : Technology & Engineering
ISBN : 9781420004106

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Hard Disk Drive by Abdullah Al Mamun,GuoXiao Guo,Chao Bi Pdf

The hard disk drive is one of the finest examples of the precision control of mechatronics, with tolerances less than one micrometer achieved while operating at high speed. Increasing demand for higher data density as well as disturbance-prone operating environments continue to test designers' mettle. Explore the challenges presented by modern hard disk drives and learn how to overcome them with Hard Disk Drive: Mechatronics and Control. Beginning with an overview of hard disk drive history, components, operating principles, and industry trends, the authors thoroughly examine the design and manufacturing challenges. They start with the head positioning servomechanism followed by the design of the actuator servo controller, the critical aspects of spindle motor control, and finally, the servo track writer, a critical technology in hard disk drive manufacturing. By comparing various design approaches for both single- and dual-stage servomechanisms, the book shows the relative pros and cons of each approach. Numerous examples and figures clarify and illustrate the discussion. Exploring practical issues such as models for plants, noise reduction, disturbances, and common problems with spindle motors, Hard Disk Drive: Mechatronics and Control avoids heavy theory in favor of providing hands-on insight into real issues facing designers every day.

Author : Shankar P. Bhattacharyya,Aniruddha Datta,Lee H. Keel
Publisher : CRC Press
Page : 679 pages
File Size : 55,8 Mb
Release : 2018-10-03
Category : Technology & Engineering
ISBN : 9781351837071

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Linear Control Theory by Shankar P. Bhattacharyya,Aniruddha Datta,Lee H. Keel Pdf

Successfully classroom-tested at the graduate level, Linear Control Theory: Structure, Robustness, and Optimization covers three major areas of control engineering (PID control, robust control, and optimal control). It provides balanced coverage of elegant mathematical theory and useful engineering-oriented results. The first part of the book develops results relating to the design of PID and first-order controllers for continuous and discrete-time linear systems with possible delays. The second section deals with the robust stability and performance of systems under parametric and unstructured uncertainty. This section describes several elegant and sharp results, such as Kharitonov’s theorem and its extensions, the edge theorem, and the mapping theorem. Focusing on the optimal control of linear systems, the third part discusses the standard theories of the linear quadratic regulator, Hinfinity and l1 optimal control, and associated results. Written by recognized leaders in the field, this book explains how control theory can be applied to the design of real-world systems. It shows that the techniques of three term controllers, along with the results on robust and optimal control, are invaluable to developing and solving research problems in many areas of engineering.

Author : Heinz H. Bauschke,Regina S. Burachik,D. Russell Luke
Publisher : Springer Nature
Page : 489 pages
File Size : 45,8 Mb
Release : 2019-11-06
Category : Mathematics
ISBN : 9783030259396

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Splitting Algorithms, Modern Operator Theory, and Applications by Heinz H. Bauschke,Regina S. Burachik,D. Russell Luke Pdf

This book brings together research articles and state-of-the-art surveys in broad areas of optimization and numerical analysis with particular emphasis on algorithms. The discussion also focuses on advances in monotone operator theory and other topics from variational analysis and nonsmooth optimization, especially as they pertain to algorithms and concrete, implementable methods. The theory of monotone operators is a central framework for understanding and analyzing splitting algorithms. Topics discussed in the volume were presented at the interdisciplinary workshop titled Splitting Algorithms, Modern Operator Theory, and Applications held in Oaxaca, Mexico in September, 2017. Dedicated to Jonathan M. Borwein, one of the most versatile mathematicians in contemporary history, this compilation brings theory together with applications in novel and insightful ways.

Author : Shankar P. Bhattacharyya,Lee H. Keel
Publisher : Cambridge University Press
Page : 697 pages
File Size : 45,8 Mb
Release : 2022-01-13
Category : Mathematics
ISBN : 9781108841689

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Linear Multivariable Control Systems by Shankar P. Bhattacharyya,Lee H. Keel Pdf

A graduate text providing broad coverage of linear multivariable control systems, including several new results and recent approaches.

Author : M. Vukobratovic,D. Stokic,N. Kircanski
Publisher : Springer Science & Business Media
Page : 394 pages
File Size : 45,7 Mb
Release : 2013-12-11
Category : Computers
ISBN : 9783642822018

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Non-Adaptive and Adaptive Control of Manipulation Robots by M. Vukobratovic,D. Stokic,N. Kircanski Pdf

The material presented in this monograph is a logical continuation of research results achieved in the control of manipulation robots. This is in a way, a synthesis of many-year research efforts of the associates of Robotics Department, Mihailo Pupin Institute, in the field of dynamic control.of robotic systems. As in Vol. 2 of this Series, all results rely on the mathematical models of dynamics of active spatial mechanisms which offer the possibility for adequate dynamic control of manipula tion robots. Compared with Vol. 2, this monograph has three essential new character istics, and a variety of new tasks arising in the control of robots which have been formulated and solved for the first time. One of these novelties is nonadaptive control synthesized for the case of large variations in payload parameters, under the condition that the practical stability of the overall system is satisfied. Such a case of control synthesis meets the actual today's needs in industrial robot applications. The second characteristic of the monograph is the efficient adaptive control algorithm based on decentralized control structure intended for tasks in which parameter variations cannot be specified in advance. To be objective, this is not the case in industrial robotics today. Thus, nonadaptive control with and without a particular parameter variation is supplemented by adaptive dynamic control algorithms which will cer tainly be applicable in the future industrial practice when parametric identification of workpieces will be required.

Author : Arthur E. Bryson
Publisher : Cambridge University Press
Page : 392 pages
File Size : 43,6 Mb
Release : 2002-08-29
Category : Mathematics
ISBN : 0521812852

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Applied Linear Optimal Control Hardback with CD-ROM by Arthur E. Bryson Pdf

CD-ROM contains: MATLAB codes of the OPTEST toolbox -- Code for examples, figures, and selected problems in text.

Author : Eric Ostertag
Publisher : Springer Science & Business Media
Page : 346 pages
File Size : 44,6 Mb
Release : 2011-01-03
Category : Technology & Engineering
ISBN : 9783642137341

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Mono- and Multivariable Control and Estimation by Eric Ostertag Pdf

This book presents the various design methods of a state-feedback control law and of an observer. The considered systems are of continuous-time and of discrete-time nature, monovariable or multivariable, the last ones being of main consideration. Three different approaches are described: • Linear design methods, with an emphasis on decoupling strategies, and a general formula for multivariable controller or observer design; • Quadratic optimization methods: Linear Quadratic Control (LQC), optimal Kalman filtering, Linear Quadratic Gaussian (LQG) control; • Linear matrix inequalities (LMIs) to solve linear and quadratic problems. The duality between control and observation is taken to advantage and extended up to the mathematical domain. A large number of exercises, all given with their detailed solutions, mostly obtained with MATLAB, reinforce and exemplify the practical orientation of this book. The programs, created by the author for their solving, are available on the Internet sites of Springer and of MathWorks for downloading. This book is targeted at students of Engineering Schools or Universities, at the Master’s level, at engineers desiring to design and implement innovative control methods, and at researchers.