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A Survey Of The Maximum Principles For Optimal Control Problems With State Constraints
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Book Synopsis A Survey of the Maximum Principles for Optimal Control Problems with State Constraints by : R. F. Hartl
Download or read book A Survey of the Maximum Principles for Optimal Control Problems with State Constraints written by R. F. Hartl and published by . This book was released on 2017 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper gives a survey of the various forms of Pontryagin's maximum principle for optimal control problems with state variable inequality constraints. The relations between the different sets of optimality conditions arising in these forms are shown. Furthermore, the application of these maximum principle conditions is demonstrated by solving some illustrative examples.
Book Synopsis A maximum principle for non-smooth optimal control problems with state contraints by : R. B. Vinter
Download or read book A maximum principle for non-smooth optimal control problems with state contraints written by R. B. Vinter and published by . This book was released on 1982 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Maximum Principle for Non-smooth Optimal Control Problems with State Contraints by : Richard B. Vinter
Download or read book A Maximum Principle for Non-smooth Optimal Control Problems with State Contraints written by Richard B. Vinter and published by . This book was released on 1980 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :University of Minnesota. Institute for Mathematics and Its Applications Publisher : ISBN 13 : Total Pages : pages Book Rating :4.:/5 (123 download)
Book Synopsis Maximum Principle for State-constrained Optimal Control Problems Governed by Quasilinear Elliptic Equations by : University of Minnesota. Institute for Mathematics and Its Applications
Download or read book Maximum Principle for State-constrained Optimal Control Problems Governed by Quasilinear Elliptic Equations written by University of Minnesota. Institute for Mathematics and Its Applications and published by . This book was released on 1992 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Maximum Principle for State-constrained Optimal Control Problems Geverned by Quasilinear Elliptic Equations by : E. Casas
Download or read book Maximum Principle for State-constrained Optimal Control Problems Geverned by Quasilinear Elliptic Equations written by E. Casas and published by . This book was released on 1992 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Optimal Control of a Double Integrator by : Arturo Locatelli
Download or read book Optimal Control of a Double Integrator written by Arturo Locatelli and published by . This book was released on 2017 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Methods for Optimal Control Problems with State Constraints by : Radoslaw Pytlak
Download or read book Numerical Methods for Optimal Control Problems with State Constraints written by Radoslaw Pytlak and published by Springer Science & Business Media. This book was released on 1999-08-19 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: While optimality conditions for optimal control problems with state constraints have been extensively investigated in the literature the results pertaining to numerical methods are relatively scarce. This book fills the gap by providing a family of new methods. Among others, a novel convergence analysis of optimal control algorithms is introduced. The analysis refers to the topology of relaxed controls only to a limited degree and makes little use of Lagrange multipliers corresponding to state constraints. This approach enables the author to provide global convergence analysis of first order and superlinearly convergent second order methods. Further, the implementation aspects of the methods developed in the book are presented and discussed. The results concerning ordinary differential equations are then extended to control problems described by differential-algebraic equations in a comprehensive way for the first time in the literature.
Book Synopsis Some Geometric Aspects of Optimal Control Problems with State Inequality Constraints by : Kenneth Var Saunders
Download or read book Some Geometric Aspects of Optimal Control Problems with State Inequality Constraints written by Kenneth Var Saunders and published by . This book was released on 1965 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis deals with the investigation of geometric aspects of optimal control problems with state inequality constraints. An 'unrestricted' maximum principle is derived, whose associated adjoint equation possesses a solution which is continuous, except under special circumstances, even at junction points of an optimal trajectory with the state boundary. This result is shown to be valid under the assumption of regularity (in the sense of Pontryagin) as well as for certain non-regular problems. The relation between the 'unrestricted' maximum principle and the restricted one of Pontryagin is demonstrated. This investigation is based on the geometric notions introduced by Blaquiere and Leitmann and constitutes an extension of their work to problems with state variable inequality constraints. This geometric approach is contrasted with the approach of Dynamic Programming. (Author).
Book Synopsis A Primer on Pontryagin's Principle in Optimal Control by : I. Michael Ross
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
Book Synopsis Applied and Computational Optimal Control by : Kok Lay Teo
Download or read book Applied and Computational Optimal Control written by Kok Lay Teo and published by Springer Nature. This book was released on 2021-05-24 with total page 581 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Optimal Control of ODEs and DAEs by : Matthias Gerdts
Download or read book Optimal Control of ODEs and DAEs written by Matthias Gerdts and published by Walter de Gruyter GmbH & Co KG. This book was released on 2023-11-06 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis On the minimum principle for optimal control problems with state constraints by : Helmut Maurer
Download or read book On the minimum principle for optimal control problems with state constraints written by Helmut Maurer and published by . This book was released on 1979 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Optimal Control Theory by : Zhongjing Ma
Download or read book Optimal Control Theory written by Zhongjing Ma and published by Springer Nature. This book was released on 2021-01-30 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on how to implement optimal control problems via the variational method. It studies how to implement the extrema of functional by applying the variational method and covers the extrema of functional with different boundary conditions, involving multiple functions and with certain constraints etc. It gives the necessary and sufficient condition for the (continuous-time) optimal control solution via the variational method, solves the optimal control problems with different boundary conditions, analyzes the linear quadratic regulator & tracking problems respectively in detail, and provides the solution of optimal control problems with state constraints by applying the Pontryagin’s minimum principle which is developed based upon the calculus of variations. And the developed results are applied to implement several classes of popular optimal control problems and say minimum-time, minimum-fuel and minimum-energy problems and so on. As another key branch of optimal control methods, it also presents how to solve the optimal control problems via dynamic programming and discusses the relationship between the variational method and dynamic programming for comparison. Concerning the system involving individual agents, it is also worth to study how to implement the decentralized solution for the underlying optimal control problems in the framework of differential games. The equilibrium is implemented by applying both Pontryagin’s minimum principle and dynamic programming. The book also analyzes the discrete-time version for all the above materials as well since the discrete-time optimal control problems are very popular in many fields.
Book Synopsis Calculus of Variations and Optimal Control Theory by : Daniel Liberzon
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
Book Synopsis Optimal Control Theory by : Suresh P. Sethi
Download or read book Optimal Control Theory written by Suresh P. Sethi and published by Springer Nature. This book was released on 2022-01-03 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new 4th edition offers an introduction to optimal control theory and its diverse applications in management science and economics. It introduces students to the concept of the maximum principle in continuous (as well as discrete) time by combining dynamic programming and Kuhn-Tucker theory. While some mathematical background is needed, the emphasis of the book is not on mathematical rigor, but on modeling realistic situations encountered in business and economics. It applies optimal control theory to the functional areas of management including finance, production and marketing, as well as the economics of growth and of natural resources. In addition, it features material on stochastic Nash and Stackelberg differential games and an adverse selection model in the principal-agent framework. Exercises are included in each chapter, while the answers to selected exercises help deepen readers’ understanding of the material covered. Also included are appendices of supplementary material on the solution of differential equations, the calculus of variations and its ties to the maximum principle, and special topics including the Kalman filter, certainty equivalence, singular control, a global saddle point theorem, Sethi-Skiba points, and distributed parameter systems. Optimal control methods are used to determine optimal ways to control a dynamic system. The theoretical work in this field serves as the foundation for the book, in which the author applies it to business management problems developed from his own research and classroom instruction. The new edition has been refined and updated, making it a valuable resource for graduate courses on applied optimal control theory, but also for financial and industrial engineers, economists, and operational researchers interested in applying dynamic optimization in their fields.
Book Synopsis Principles of Optimal Control Theory by : R. Gamkrelidze
Download or read book Principles of Optimal Control Theory written by R. Gamkrelidze and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the late 1950's, the group of Soviet mathematicians consisting of L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko made fundamental contributions to optimal control theory. Much of their work was collected in their monograph, The Mathematical Theory of Optimal Processes. Subsequently, Professor Gamkrelidze made further important contributions to the theory of necessary conditions for problems of optimal control and general optimization problems. In the present monograph, Professor Gamkrelidze presents his current view of the fundamentals of optimal control theory. It is intended for use in a one-semester graduate course or advanced undergraduate course. We are now making these ideas available in English to all those interested in optimal control theory. West Lafayette, Indiana, USA Leonard D. Berkovitz Translation Editor Vll Preface This book is based on lectures I gave at the Tbilisi State University during the fall of 1974. It contains, in essence, the principles of general control theory and proofs of the maximum principle and basic existence theorems of optimal control theory. Although the proofs of the basic theorems presented here are far from being the shortest, I think they are fully justified from the conceptual view point. In any case, the notions we introduce and the methods developed have one unquestionable advantage -they are constantly used throughout control theory, and not only for the proofs of the theorems presented in this book.
Book Synopsis Some Aspects of State Constrained Optimal Control Problems by : Francois Xavier Litt
Download or read book Some Aspects of State Constrained Optimal Control Problems written by Francois Xavier Litt and published by . This book was released on 1971 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt:
