A Primer On Pontryagin S Principle In Optimal Control

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A Primer On Pontryagin S Principle In Optimal Control

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Author : I. Michael Ross
language : en
Publisher:
Release Date : 2009

A Primer On Pontryagin S Principle In Optimal Control written by I. Michael Ross and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Technology & Engineering categories.

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

Primer On Optimal Control Theory

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Author : Jason L. Speyer
language : en
Publisher: SIAM
Release Date : 2010-05-13

Primer On Optimal Control Theory written by Jason L. Speyer and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-05-13 with Mathematics categories.

A rigorous introduction to optimal control theory, which will enable engineers and scientists to put the theory into practice.

Primer On Optimal Control Theory

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Author : Jason L. Speyer
language : en
Publisher: SIAM
Release Date : 2010-01-01

Primer On Optimal Control Theory written by Jason L. Speyer and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-01 with Mathematics categories.

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.

Applied Optimal Control

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Author : A. E. Bryson
language : en
Publisher: Routledge
Release Date : 2018-05-04

Applied Optimal Control written by A. E. Bryson and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-04 with Technology & Engineering categories.

This best-selling text focuses on the analysis and design of complicated dynamics systems. CHOICE called it ""a high-level, concise book that could well be used as a reference by engineers, applied mathematicians, and undergraduates. The format is good, the presentation clear, the diagrams instructive, the examples and problems helpful...References and a multiple-choice examination are included.

Optimal Control With Aerospace Applications

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Author : James M Longuski
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-04

Optimal Control With Aerospace Applications written by James M Longuski 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 2013-11-04 with Technology & Engineering categories.

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!

A Primer On The Calculus Of Variations And Optimal Control Theory

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Author : Mike Mesterton-Gibbons
language : en
Publisher: American Mathematical Soc.
Release Date : 2009

A Primer On The Calculus Of Variations And Optimal Control Theory written by Mike Mesterton-Gibbons and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.

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.

Energy Efficient Train Control

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Author : Philip G. Howlett
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Energy Efficient Train Control written by Philip G. Howlett 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 Technology & Engineering categories.

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.

The Sequential Quadratic Hamiltonian Method

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Author : Alfio Borzì
language : en
Publisher: CRC Press
Release Date : 2023-05-26

The Sequential Quadratic Hamiltonian Method written by Alfio Borzì and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-26 with Mathematics categories.

The sequential quadratic hamiltonian (SQH) method is a novel numerical optimization procedure for solving optimal control problems governed by differential models. It is based on the characterisation of optimal controls in the framework of the Pontryagin maximum principle (PMP). The SQH method is a powerful computational methodology that is capable of development in many directions. The Sequential Quadratic Hamiltonian Method: Solving Optimal Control Problems discusses its analysis and use in solving nonsmooth ODE control problems, relaxed ODE control problems, stochastic control problems, mixed-integer control problems, PDE control problems, inverse PDE problems, differential Nash game problems, and problems related to residual neural networks. This book may serve as a textbook for undergraduate and graduate students, and as an introduction for researchers in sciences and engineering who intend to further develop the SQH method or wish to use it as a numerical tool for solving challenging optimal control problems and for investigating the Pontryagin maximum principle on new optimisation problems. Features Provides insight into mathematical and computational issues concerning optimal control problems, while discussing many differential models of interest in different disciplines. Suitable for undergraduate and graduate students and as an introduction for researchers in sciences and engineering. Accompanied by codes which allow the reader to apply the SQH method to solve many different optimal control and optimisation problems.

Calculus Of Variations And Optimal Control Theory

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Author : Daniel Liberzon
language : en
Publisher: Princeton University Press
Release Date : 2012

Calculus Of Variations And Optimal Control Theory written by Daniel Liberzon and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.

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

Advanced Motion Control And Navigation Of Robots In Extreme Environments

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Author : Allahyar Montazeri
language : en
Publisher: Frontiers Media SA
Release Date : 2024-11-20

Advanced Motion Control And Navigation Of Robots In Extreme Environments written by Allahyar Montazeri and has been published by Frontiers Media SA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-20 with Technology & Engineering categories.

Advances in robotics and autonomous systems have opened new horizons for the scientists by creating new opportunities to explore extreme environments that would previously not have been possible. For example, robots that are deployed to study environmental processes such remote volcanos, monitor the climate variables under the adverse weather conditions, understand underground mines, and explore deep oceans which are all inaccessible or hazardous for the human. Industrial applications can also often be situated in extreme environments such as offshore oil and gas and nuclear industries. In such applications the autonomous robot is expected to complete tasks such as repair and maintenance, exploration, reconnaissance, inspection, and transportation which is either done in isolation or as a team of cooperative robots. Due to the harsh and severe conditions of such environments, designing an advanced robotic system that can endure them is a challenging task. The robot needs to cope with the time-varying, restricted, uncertain, and unstructured nature of the environment to achieve the planning and execution of the tasks. This in turn demands development of advanced, robust and adaptive motion control and navigation algorithms along with machine learning and deep learning algorithms with high cognitive capability for the robot to perceive the surrounding environment effectively. The use of both single and multi-robot platforms can be advantageous depending on the specific application and environment.