Problems And Methods Of Optimal Control

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Numerical Methods for Optimal Control Problems with State Constraints

Radoslaw Pytlak
Numerical Methods for Optimal Control Problems with State Constraints Book PDF

Author : Radoslaw Pytlak
Publisher : Springer Science & Business Media
Page : 244 pages
File Size : 51,5 Mb
Release : 1999-08-19
Category : Science
ISBN : 3540662146

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Numerical Methods for Optimal Control Problems with State Constraints by Radoslaw Pytlak Pdf

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.

Numerical Methods for Optimal Control Problems

Maurizio Falcone,Roberto Ferretti,Lars Grüne,William M. McEneaney
Numerical Methods for Optimal Control Problems Book PDF

Author : Maurizio Falcone,Roberto Ferretti,Lars Grüne,William M. McEneaney
Publisher : Springer
Page : 0 pages
File Size : 54,5 Mb
Release : 2019-02-05
Category : Science
ISBN : 3030019586

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Numerical Methods for Optimal Control Problems by Maurizio Falcone,Roberto Ferretti,Lars Grüne,William M. McEneaney Pdf

This work presents recent mathematical methods in the area of optimal control with a particular emphasis on the computational aspects and applications. Optimal control theory concerns the determination of control strategies for complex dynamical systems, in order to optimize some measure of their performance. Started in the 60's under the pressure of the "space race" between the US and the former USSR, the field now has a far wider scope, and embraces a variety of areas ranging from process control to traffic flow optimization, renewable resources exploitation and management of financial markets. These emerging applications require more and more efficient numerical methods for their solution, a very difficult task due the huge number of variables. The chapters of this volume give an up-to-date presentation of several recent methods in this area including fast dynamic programming algorithms, model predictive control and max-plus techniques. This book is addressed to researchers, graduate students and applied scientists working in the area of control problems, differential games and their applications.

Global Methods in Optimal Control Theory

Vadim Krotov
Global Methods in Optimal Control Theory Book PDF

Author : Vadim Krotov
Publisher : CRC Press
Page : 410 pages
File Size : 50,8 Mb
Release : 1995-10-13
Category : Mathematics
ISBN : 0824793293

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Global Methods in Optimal Control Theory by Vadim Krotov Pdf

This work describes all basic equaitons and inequalities that form the necessary and sufficient optimality conditions of variational calculus and the theory of optimal control. Subjects addressed include developments in the investigation of optimality conditions, new classes of solutions, analytical and computation methods, and applications.

Practical Methods for Optimal Control and Estimation Using Nonlinear Programming

John T. Betts
Practical Methods for Optimal Control and Estimation Using Nonlinear Programming Book PDF

Author : John T. Betts
Publisher : SIAM
Page : 442 pages
File Size : 48,7 Mb
Release : 2010-01-01
Category : Mathematics
ISBN : 9780898716887

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Practical Methods for Optimal Control and Estimation Using Nonlinear Programming by John T. Betts Pdf

A focused presentation of how sparse optimization methods can be used to solve optimal control and estimation problems.

Geometric Optimal Control

Heinz Schättler,Urszula Ledzewicz
Geometric Optimal Control Book PDF

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.

Optimal Control

Bulirsch,Miele,Stoer,Well
Optimal Control Book PDF

Author : Bulirsch,Miele,Stoer,Well
Publisher : Birkhäuser
Page : 352 pages
File Size : 48,5 Mb
Release : 2013-03-08
Category : Science
ISBN : 9783034875394

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Optimal Control by Bulirsch,Miele,Stoer,Well Pdf

"Optimal Control" reports on new theoretical and practical advances essential for analysing and synthesizing optimal controls of dynamical systems governed by partial and ordinary differential equations. New necessary and sufficient conditions for optimality are given. Recent advances in numerical methods are discussed. These have been achieved through new techniques for solving large-sized nonlinear programs with sparse Hessians, and through a combination of direct and indirect methods for solving the multipoint boundary value problem. The book also focuses on the construction of feedback controls for nonlinear systems and highlights advances in the theory of problems with uncertainty. Decomposition methods of nonlinear systems and new techniques for constructing feedback controls for state- and control constrained linear quadratic systems are presented. The book offers solutions to many complex practical optimal control problems.

Optimal Control of Random Sequences in Problems with Constraints

A.B. Piunovskiy
Optimal Control of Random Sequences in Problems with Constraints Book PDF

Author : A.B. Piunovskiy
Publisher : Springer Science & Business Media
Page : 355 pages
File Size : 53,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401155083

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Optimal Control of Random Sequences in Problems with Constraints by A.B. Piunovskiy Pdf

Controlled stochastic processes with discrete time form a very interest ing and meaningful field of research which attracts widespread attention. At the same time these processes are used for solving of many applied problems in the queueing theory, in mathematical economics. in the theory of controlled technical systems, etc. . In this connection, methods of the theory of controlled processes constitute the every day instrument of many specialists working in the areas mentioned. The present book is devoted to the rather new area, that is, to the optimal control theory with functional constraints. This theory is close to the theory of multicriteria optimization. The compromise between the mathematical rigor and the big number of meaningful examples makes the book attractive for professional mathematicians and for specialists who ap ply mathematical methods in different specific problems. Besides. the book contains setting of many new interesting problems for further invf'stigatioll. The book can form the basis of special courses in the theory of controlled stochastic processes for students and post-graduates specializing in the ap plied mathematics and in the control theory of complex systf'ms. The grounding of graduating students of mathematical department is sufficient for the perfect understanding of all the material. The book con tains the extensive Appendix where the necessary knowledge ill Borel spaces and in convex analysis is collected. All the meaningful examples can be also understood by readers who are not deeply grounded in mathematics.

Counterexamples in Optimal Control Theory

S. I︠A︡ Serovaĭskiĭ
Counterexamples in Optimal Control Theory Book PDF

Author : S. I︠A︡ Serovaĭskiĭ
Publisher : Walter de Gruyter
Page : 192 pages
File Size : 46,8 Mb
Release : 2004
Category : Mathematics
ISBN : 9067644005

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Counterexamples in Optimal Control Theory by S. I︠A︡ Serovaĭskiĭ Pdf

This monograph deals with cases where optimal control either does not exist or is not unique, cases where optimality conditions are insufficient of degenerate, or where extremum problems in the sense of Tikhonov and Hadamard are ill-posed, and other situations. A formal application of classical optimisation methods in such cases either leads to wrong results or has no effect. The detailed analysis of these examples should provide a better understanding of the modern theory of optimal control and the practical difficulties of solving extremum problems.

Optimal Control of Partial Differential Equations

Fredi Tröltzsch
Optimal Control of Partial Differential Equations Book PDF

Author : Fredi Tröltzsch
Publisher : American Mathematical Society
Page : 417 pages
File Size : 44,5 Mb
Release : 2024-03-21
Category : Mathematics
ISBN : 9781470476441

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Optimal Control of Partial Differential Equations by Fredi Tröltzsch Pdf

Optimal control theory is concerned with finding control functions that minimize cost functions for systems described by differential equations. The methods have found widespread applications in aeronautics, mechanical engineering, the life sciences, and many other disciplines. This book focuses on optimal control problems where the state equation is an elliptic or parabolic partial differential equation. Included are topics such as the existence of optimal solutions, necessary optimality conditions and adjoint equations, second-order sufficient conditions, and main principles of selected numerical techniques. It also contains a survey on the Karush-Kuhn-Tucker theory of nonlinear programming in Banach spaces. The exposition begins with control problems with linear equations, quadratic cost functions and control constraints. To make the book self-contained, basic facts on weak solutions of elliptic and parabolic equations are introduced. Principles of functional analysis are introduced and explained as they are needed. Many simple examples illustrate the theory and its hidden difficulties. This start to the book makes it fairly self-contained and suitable for advanced undergraduates or beginning graduate students. Advanced control problems for nonlinear partial differential equations are also discussed. As prerequisites, results on boundedness and continuity of solutions to semilinear elliptic and parabolic equations are addressed. These topics are not yet readily available in books on PDEs, making the exposition also interesting for researchers. Alongside the main theme of the analysis of problems of optimal control, Tröltzsch also discusses numerical techniques. The exposition is confined to brief introductions into the basic ideas in order to give the reader an impression of how the theory can be realized numerically. After reading this book, the reader will be familiar with the main principles of the numerical analysis of PDE-constrained optimization.

Numerical Methods for Stochastic Control Problems in Continuous Time

Harold Kushner,Paul G. Dupuis
Numerical Methods for Stochastic Control Problems in Continuous Time Book PDF

Author : Harold Kushner,Paul G. Dupuis
Publisher : Springer Science & Business Media
Page : 480 pages
File Size : 48,8 Mb
Release : 2013-11-27
Category : Mathematics
ISBN : 9781461300076

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Numerical Methods for Stochastic Control Problems in Continuous Time by Harold Kushner,Paul G. Dupuis Pdf

Stochastic control is a very active area of research. This monograph, written by two leading authorities in the field, has been updated to reflect the latest developments. It covers effective numerical methods for stochastic control problems in continuous time on two levels, that of practice and that of mathematical development. It is broadly accessible for graduate students and researchers.

Numerical Methods for Optimal Control Problems

Maurizio Falcone,Roberto Ferretti,Lars Grüne,William M. McEneaney
Numerical Methods for Optimal Control Problems Book PDF

Author : Maurizio Falcone,Roberto Ferretti,Lars Grüne,William M. McEneaney
Publisher : Springer
Page : 275 pages
File Size : 51,6 Mb
Release : 2019-01-26
Category : Science
ISBN : 9783030019594

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Numerical Methods for Optimal Control Problems by Maurizio Falcone,Roberto Ferretti,Lars Grüne,William M. McEneaney Pdf

This work presents recent mathematical methods in the area of optimal control with a particular emphasis on the computational aspects and applications. Optimal control theory concerns the determination of control strategies for complex dynamical systems, in order to optimize some measure of their performance. Started in the 60's under the pressure of the "space race" between the US and the former USSR, the field now has a far wider scope, and embraces a variety of areas ranging from process control to traffic flow optimization, renewable resources exploitation and management of financial markets. These emerging applications require more and more efficient numerical methods for their solution, a very difficult task due the huge number of variables. The chapters of this volume give an up-to-date presentation of several recent methods in this area including fast dynamic programming algorithms, model predictive control and max-plus techniques. This book is addressed to researchers, graduate students and applied scientists working in the area of control problems, differential games and their applications.

Numerical Methods for Optimal Control Problems with State Constraints

Radoslaw Pytlak
Numerical Methods for Optimal Control Problems with State Constraints Book PDF

Author : Radoslaw Pytlak
Publisher : Springer
Page : 224 pages
File Size : 46,8 Mb
Release : 2006-11-14
Category : Science
ISBN : 9783540486626

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Numerical Methods for Optimal Control Problems with State Constraints by Radoslaw Pytlak Pdf

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.

Computational Methods in Optimal Control Problems

I.H. Mufti
Computational Methods in Optimal Control Problems Book PDF

Author : I.H. Mufti
Publisher : Springer Science & Business Media
Page : 54 pages
File Size : 49,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642859601

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Computational Methods in Optimal Control Problems by I.H. Mufti Pdf

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.

Advances in Nonlinear Dynamics and Control: A Report from Russia

Alexander B. Kurzhanski
Advances in Nonlinear Dynamics and Control A Report from Russia Book PDF

Author : Alexander B. Kurzhanski
Publisher : Springer Science & Business Media
Page : 286 pages
File Size : 50,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461203490

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Advances in Nonlinear Dynamics and Control: A Report from Russia by Alexander B. Kurzhanski Pdf

The purpose of this volume is to present a coherent collection of overviews of recent Russian research in Control Theory and Nonlinear Dynamics written by active investigators in these fields. It is needless to say that the contribution of the scientists of the former Soviet Union to the development of nonlinear dynamics and control was significant and that their scientific schools and research community have highly evolved points of view, accents and depth which complemented, enhanced and sometimes inspired research directions in the West. With scientific exchange strongly increasing, there is still a consider able number of Eastern publications unknown to the Western community. We have therefore encouraged the authors to produce extended bibliogra phies in their papers. The particular emphasis of this volume is on the treatment of uncer tain systems in a deterministic setting-a field highly developed in the former Soviet Union and actively investigated in the West. The topics are concentrated around the three main branches of un certain dynamics which are the theory of Differential Games, the set membership approach to Evolution, Estimation and Control and the the ory of Robust Stabilization. The application of these techniques to non linear systems as well as the global optimization of the latter are also among the issues treated in this volume.

Problems and Methods of Optimal Control

L.D. Akulenko
Problems and Methods of Optimal Control Book PDF

Author : L.D. Akulenko
Publisher : Springer
Page : 344 pages
File Size : 43,7 Mb
Release : 2011-10-06
Category : Mathematics
ISBN : 9401111952

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Problems and Methods of Optimal Control by L.D. Akulenko Pdf

The numerous applications of optimal control theory have given an incentive to the development of approximate techniques aimed at the construction of control laws and the optimization of dynamical systems. These constructive approaches rely on small parameter methods (averaging, regular and singular perturbations), which are well-known and have been proven to be efficient in nonlinear mechanics and optimal control theory (maximum principle, variational calculus and dynamic programming). An essential feature of the procedures for solving optimal control problems consists in the necessity for dealing with two-point boundary-value problems for nonlinear and, as a rule, nonsmooth multi-dimensional sets of differential equations. This circumstance complicates direct applications of the above-mentioned perturbation methods which have been developed mostly for investigating initial-value (Cauchy) problems. There is now a need for a systematic presentation of constructive analytical per turbation methods relevant to optimal control problems for nonlinear systems. The purpose of this book is to meet this need in the English language scientific literature and to present consistently small parameter techniques relating to the constructive investigation of some classes of optimal control problems which often arise in prac tice. This book is based on a revised and modified version of the monograph: L. D. Akulenko "Asymptotic methods in optimal control". Moscow: Nauka, 366 p. (in Russian).