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Author: Semen Ya. Serovaiskii
Publisher: Walter de Gruyter
ISBN: 3110915537
Category : Mathematics
Languages : en
Pages : 185
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Book Description
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.
Author: Semen Ya. Serovaiskii
Publisher: Walter de Gruyter
ISBN: 3110915537
Category : Mathematics
Languages : en
Pages : 185
Get Book
Book Description
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.
Author: Shanjian Tang
Publisher: World Scientific
ISBN: 9812790551
Category : Mathematics
Languages : en
Pages : 420
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Book Description
Xunjing Li (1935OCo2003) was a pioneer in control theory in China. He was known in the Chinese community of applied mathematics, and in the global community of optimal control theory of distributed parameter systems. He has made important contributions to the optimal control theory of distributed parameter systems, in particular regarding the first-order necessary conditions (Pontryagin-type maximum principle) for optimal control of nonlinear infinite-dimensional systems. He directed the Seminar of Control Theory at Fudan towards stochastic control theory in 1980s, and mathematical finance in 1990s, which has led to several important subsequent developments in both closely interactive fields. These remarkable efforts in scientific research and education, among others, gave birth to the so-called OC Fudan SchoolOCO. This proceedings volume includes a collection of original research papers or reviews authored or co-authored by Xunjing Li''s former students, postdoctoral fellows, and mentored scholars in the areas of control theory, dynamic systems, mathematical finance, and stochastic analysis, among others. Sample Chapter(s). Part 1: A Tribute in Memory of Professor Xunjing Li on His Seventieth Birthday (112 KB). Contents: Stochastic Control, Mathematical Finance, and Backward Stochastic Differential Equations: Axiomatic Characteristics for Solutions of Reflected Backward Stochastic Differential Equations (X Bao & S Tang); A Linear Quadratic Optimal Control Problem for Stochastic Volterra Integral Equations (S Chen & J Yong); Stochastic Control and BSDEs with Quadratic Growth (M Fuhrman et al.); Unique Continuation and Observability for Stochastic Parabolic Equations and Beyond (X Zhang); Deterministic Control Systems: Some Counterexamples in Existence Theory of Optimal Control (H Lou); A Generalized Framework for Global Output Feedback Stabilization of Inherently Nonlinear Systems with Uncertainties (J Polendo & C Qian); On Finite-Time Stabilization of a Class of Nonsmoothly Stabilizable Systems (B Yang & W Lin); Dynamics and Optimal Control of Partial Differential Equations: Optimal Control of Quasilinear Elliptic Obstacle Problems (Q Chen & Y Ye); Controllability of a Nonlinear Degenerate Parabolic System with Bilinear Control (P Lin et al.); and other papers. Readership: Researchers and graduate students in the areas of control theory, mathematical finance and dynamical systems."
Author: Vadim Krotov
Publisher: CRC Press
ISBN: 9780824793296
Category : Mathematics
Languages : en
Pages : 410
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Book Description
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.
Author: Jack Macki
Publisher: Springer Science & Business Media
ISBN: 1461256712
Category : Science
Languages : en
Pages : 179
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Book Description
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].
Author: Suzanne Lenhart
Publisher: CRC Press
ISBN: 1584886404
Category : Mathematics
Languages : en
Pages : 272
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Book Description
From economics and business to the biological sciences to physics and engineering, professionals successfully use the powerful mathematical tool of optimal control to make management and strategy decisions. Optimal Control Applied to Biological Models thoroughly develops the mathematical aspects of optimal control theory and provides insight into the application of this theory to biological models. Focusing on mathematical concepts, the book first examines the most basic problem for continuous time ordinary differential equations (ODEs) before discussing more complicated problems, such as variations of the initial conditions, imposed bounds on the control, multiple states and controls, linear dependence on the control, and free terminal time. In addition, the authors introduce the optimal control of discrete systems and of partial differential equations (PDEs). Featuring a user-friendly interface, the book contains fourteen interactive sections of various applications, including immunology and epidemic disease models, management decisions in harvesting, and resource allocation models. It also develops the underlying numerical methods of the applications and includes the MATLAB® codes on which the applications are based. Requiring only basic knowledge of multivariable calculus, simple ODEs, and mathematical models, this text shows how to adjust controls in biological systems in order to achieve proper outcomes.
Author: David N. Burghes
Publisher:
ISBN:
Category : Science
Languages : en
Pages : 408
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Book Description
Author: L.D. Berkovitz
Publisher: Springer Science & Business Media
ISBN: 1475760973
Category : Mathematics
Languages : en
Pages : 315
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Book Description
This book is an introduction to the mathematical theory of optimal control of processes governed by ordinary differential eq- tions. It is intended for students and professionals in mathematics and in areas of application who want a broad, yet relatively deep, concise and coherent introduction to the subject and to its relati- ship with applications. In order to accommodate a range of mathema- cal interests and backgrounds among readers, the material is arranged so that the more advanced mathematical sections can be omitted wi- out loss of continuity. For readers primarily interested in appli- tions a recommended minimum course consists of Chapter I, the sections of Chapters II, III, and IV so recommended in the introductory sec tions of those chapters, and all of Chapter V. The introductory sec tion of each chapter should further guide the individual reader toward material that is of interest to him. A reader who has had a good course in advanced calculus should be able to understand the defini tions and statements of the theorems and should be able to follow a substantial portion of the mathematical development. The entire book can be read by someone familiar with the basic aspects of Lebesque integration and functional analysis. For the reader who wishes to find out more about applications we recommend references [2], [13], [33], [35], and [50], of the Bibliography at the end of the book.
Author: William W. Hager
Publisher: Springer Science & Business Media
ISBN: 1475760957
Category : Technology & Engineering
Languages : en
Pages : 529
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Book Description
February 27 - March 1, 1997, the conference Optimal Control: The ory, Algorithms, and Applications took place at the University of Florida, hosted by the Center for Applied Optimization. The conference brought together researchers from universities, industry, and government laborato ries in the United States, Germany, Italy, France, Canada, and Sweden. There were forty-five invited talks, including seven talks by students. The conference was sponsored by the National Science Foundation and endorsed by the SIAM Activity Group on Control and Systems Theory, the Mathe matical Programming Society, the International Federation for Information Processing (IFIP), and the International Association for Mathematics and Computers in Simulation (IMACS). Since its inception in the 1940s and 1950s, Optimal Control has been closely connected to industrial applications, starting with aerospace. The program for the Gainesville conference, which reflected the rich cross-disci plinary flavor of the field, included aerospace applications as well as both novel and emerging applications to superconductors, diffractive optics, non linear optics, structural analysis, bioreactors, corrosion detection, acoustic flow, process design in chemical engineering, hydroelectric power plants, sterilization of canned foods, robotics, and thermoelastic plates and shells. The three days of the conference were organized around the three confer ence themes, theory, algorithms, and applications. This book is a collection of the papers presented at the Gainesville conference. We would like to take this opportunity to thank the sponsors and participants of the conference, the authors, the referees, and the publisher for making this volume possible.
Author: Heinz Schättler
Publisher: Springer Science & Business Media
ISBN: 1461438349
Category : Mathematics
Languages : en
Pages : 652
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Book Description
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: Simon Serovajsky
Publisher: CRC Press
ISBN: 1040089216
Category : Mathematics
Languages : en
Pages : 657
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Book Description
Optimization: 100 Examples is a book devoted to the analysis of scenarios for which the use of well-known optimization methods encounter certain difficulties. Analysing such examples allows a deeper understanding of the features of these optimization methods, including the limits of their applicability. In this way, the book seeks to stimulate further development and understanding of the theory of optimal control. The study of the presented examples makes it possible to more effectively diagnose problems that arise in the practical solution of optimal control problems, and to find ways to overcome the difficulties that have arisen. Features Vast collection of examples Simple. accessible presentation Suitable as a research reference for anyone with an interest in optimization and optimal control theory, including mathematicians and engineers Examples differ in properties, i.e. each effect for each class of problems is illustrated by a unique example. Simon Serovajsky is a professor of mathematics at Al-Farabi Kazakh National University in Kazakhstan. He is the author of many books published in the area of optimization and optimal control theory, mathematical physics, mathematical modelling, philosophy and history of mathematics as well as a long list of high-quality publications in learned journals.
