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| the mathematical theory of optimal processes: Mathematical Theory of Optimal Processes L.S. Pontryagin, 1987-03-06 The fourth and final volume in this comprehensive set presents the maximum principle as a wide ranging solution to nonclassical, variational problems. This one mathematical method can be applied in a variety of situations, including linear equations with variable coefficients, optimal processes with delay, and the jump condition. As with the three preceding volumes, all the material contained with the 42 sections of this volume is made easily accessible by way of numerous examples, both concrete and abstract in nature. |
| the mathematical theory of optimal processes: Mathematical Theory of Optimal Processes L.S. Pontryagin, 1987-03-06 The fourth and final volume in this comprehensive set presents the maximum principle as a wide ranging solution to nonclassical, variational problems. This one mathematical method can be applied in a variety of situations, including linear equations with variable coefficients, optimal processes with delay, and the jump condition. As with the three preceding volumes, all the material contained with the 42 sections of this volume is made easily accessible by way of numerous examples, both concrete and abstract in nature. |
| the mathematical theory of optimal processes: The Mathematical Theory of Optimal Processes Lev Semenovich Pontri͡agin, Lev Semenovich Pontri︠a︡gin, 1962 |
| the mathematical theory of optimal processes: Математическая Теория Оптимальных Процессов. The Mathematical Theory of Optimal Processes. Translated by D.E. Brown. By L.S. Pontryagin, V.G. Boltyansky, R.V. Gamkrelidze and E.F. Mishchenko. Lev Semenovich PONTRYAGIN, Vladimir Grigor'evich BOLTYANSKY, R. V. Gamkrelidze, E. F. Mishchenko, 1964 |
| the mathematical theory of optimal processes: Mathematical Theory of Optimal Processes L.S. Pontryagin, 2018-05-03 The fourth and final volume in this comprehensive set presents the maximum principle as a wide ranging solution to nonclassical, variational problems. This one mathematical method can be applied in a variety of situations, including linear equations with variable coefficients, optimal processes with delay, and the jump condition. As with the three preceding volumes, all the material contained with the 42 sections of this volume is made easily accessible by way of numerous examples, both concrete and abstract in nature. |
| the mathematical theory of optimal processes: The Mathematical Theory of Optimal Processes , 1995 |
| the mathematical theory of optimal processes: Mathematical Theory of Optimal Processes L.S. Pontryagin, 1987-03-06 The fourth and final volume in this comprehensive set presents the maximum principle as a wide ranging solution to nonclassical, variational problems. This one mathematical method can be applied in a variety of situations, including linear equations with variable coefficients, optimal processes with delay, and the jump condition. As with the three preceding volumes, all the material contained with the 42 sections of this volume is made easily accessible by way of numerous examples, both concrete and abstract in nature. |
| the mathematical theory of optimal processes: The Mathematical Theory of Optimal Processes Lev Semenovich Pontri︠a︡gin, 1964 |
| the mathematical theory of optimal processes: The Mathematical Theory of Optimal Processes Lev Semenovich Pontri͡agin, 1964 |
| the mathematical theory of optimal processes: The Mathematical Theory of Optimal Processes Lev Semenovich Pontri͡agin, 1964 |
| the mathematical theory of optimal processes: Mathematical Theory of Optimal Processes L.S. Pontryagin, 1987-03-06 The fourth and final volume in this comprehensive set presents the maximum principle as a wide ranging solution to nonclassical, variational problems. This one mathematical method can be applied in a variety of situations, including linear equations with variable coefficients, optimal processes with delay, and the jump condition. As with the three preceding volumes, all the material contained with the 42 sections of this volume is made easily accessible by way of numerous examples, both concrete and abstract in nature. |
| the mathematical theory of optimal processes: The mathematical theory of optimal processes Lev Semenovich Pontriagin, 1962 |
| the mathematical theory of optimal processes: The Mathematical Theory of Optimal Processes Fred I. Greenstein, 1964 |
| the mathematical theory of optimal processes: The Mathematical Theory of Optimal Processes Lev Semenovǐc Pontryagin, 1964 |
| the mathematical theory of optimal processes: The Mathematical Theory of Optimal Processes Lev Semenovich Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, 1962 |
| the mathematical theory of optimal processes: The mathematical theory of optimal processes L. Pantryagin, 1962 |
| the mathematical theory of optimal processes: The Mathematical Theory of Optimal Processes , 1964 |
| the mathematical theory of optimal processes: Optimal Control Theory L.D. Berkovitz, 2010-12-03 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. |
| the mathematical theory of optimal processes: Nonlinear Optimal Control Theory Leonard David Berkovitz, Negash G. Medhin, 2012-08-25 Nonlinear Optimal Control Theory presents a deep, wide-ranging introduction to the mathematical theory of the optimal control of processes governed by ordinary differential equations and certain types of differential equations with memory. Many examples illustrate the mathematical issues that need to be addressed when using optimal control techniques in diverse areas. Drawing on classroom-tested material from Purdue University and North Carolina State University, the book gives a unified account of bounded state problems governed by ordinary, integrodifferential, and delay systems. It also discusses Hamilton-Jacobi theory. By providing a sufficient and rigorous treatment of finite dimensional control problems, the book equips readers with the foundation to deal with other types of control problems, such as those governed by stochastic differential equations, partial differential equations, and differential games. |
| the mathematical theory of optimal processes: Optimal Stopping and Free-Boundary Problems Goran Peskir, Albert Shiryaev, 2006-11-10 This book discloses a fascinating connection between optimal stopping problems in probability and free-boundary problems. It focuses on key examples and the theory of optimal stopping is exposed at its basic principles in discrete and continuous time covering martingale and Markovian methods. Methods of solution explained range from change of time, space, and measure, to more recent ones such as local time-space calculus and nonlinear integral equations. A chapter on stochastic processes makes the material more accessible. The book will appeal to those wishing to master stochastic calculus via fundamental examples. Areas of application include financial mathematics, financial engineering, and mathematical statistics. |
| the mathematical theory of optimal processes: The Mathematical Theory of Optimal Processes, USSR Lev Semenovich Pontri︠a︡gin, 1962 |
| the mathematical theory of optimal processes: Optimal Control of Nonlinear Processes Dieter Grass, Jonathan P. Caulkins, Gustav Feichtinger, Gernot Tragler, Doris A. Behrens, 2008-07-24 Dynamic optimization is rocket science – and more. This volume teaches researchers and students alike to harness the modern theory of dynamic optimization to solve practical problems. These problems not only cover those in space flight, but also in emerging social applications such as the control of drugs, corruption, and terror. This volume is designed to be a lively introduction to the mathematics and a bridge to these hot topics in the economics of crime for current scholars. The authors celebrate Pontryagin’s Maximum Principle – that crowning intellectual achievement of human understanding. The rich theory explored here is complemented by numerical methods available through a companion web site. |
| the mathematical theory of optimal processes: Optimal Control Theory Donald E. Kirk, 2012-04-26 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. |
| the mathematical theory of optimal processes: Linear Systems Theory João P. Hespanha, 2018-02-13 A fully updated textbook on linear systems theory Linear systems theory is the cornerstone of control theory and a well-established discipline that focuses on linear differential equations from the perspective of control and estimation. This updated second edition of Linear Systems Theory covers the subject's key topics in a unique lecture-style format, making the book easy to use for instructors and students. João Hespanha looks at system representation, stability, controllability and state feedback, observability and state estimation, and realization theory. He provides the background for advanced modern control design techniques and feedback linearization and examines advanced foundational topics, such as multivariable poles and zeros and LQG/LQR. The textbook presents only the most essential mathematical derivations and places comments, discussion, and terminology in sidebars so that readers can follow the core material easily and without distraction. Annotated proofs with sidebars explain the techniques of proof construction, including contradiction, contraposition, cycles of implications to prove equivalence, and the difference between necessity and sufficiency. Annotated theoretical developments also use sidebars to discuss relevant commands available in MATLAB, allowing students to understand these tools. This second edition contains a large number of new practice exercises with solutions. Based on typical problems, these exercises guide students to succinct and precise answers, helping to clarify issues and consolidate knowledge. The book's balanced chapters can each be covered in approximately two hours of lecture time, simplifying course planning and student review. Easy-to-use textbook in unique lecture-style format Sidebars explain topics in further detail Annotated proofs and discussions of MATLAB commands Balanced chapters can each be taught in two hours of course lecture New practice exercises with solutions included |
| the mathematical theory of optimal processes: Primer on Optimal Control Theory Jason L. Speyer, David H. Jacobson, 2010-05-13 A rigorous introduction to optimal control theory, which will enable engineers and scientists to put the theory into practice. |
| the mathematical theory of optimal processes: Theory and Applications of Stochastic Processes Zeev Schuss, 2009-12-09 Stochastic processes and diffusion theory are the mathematical underpinnings of many scientific disciplines, including statistical physics, physical chemistry, molecular biophysics, communications theory and many more. Many books, reviews and research articles have been published on this topic, from the purely mathematical to the most practical. This book offers an analytical approach to stochastic processes that are most common in the physical and life sciences, as well as in optimal control and in the theory of filltering of signals from noisy measurements. Its aim is to make probability theory in function space readily accessible to scientists trained in the traditional methods of applied mathematics, such as integral, ordinary, and partial differential equations and asymptotic methods, rather than in probability and measure theory. |
| the mathematical theory of optimal processes: Optimal Control for Chemical Engineers Simant Ranjan Upreti, 2016-04-19 This self-contained book gives a detailed treatment of optimal control theory that enables readers to formulate and solve optimal control problems. With a strong emphasis on problem solving, it provides all the necessary mathematical analyses and derivations of important results, including multiplier theorems and Pontryagin's principle. The text presents various examples and basic concepts of optimal control and describes important numerical methods and computational algorithms for solving a wide range of optimal control problems, including periodic processes. |
| the mathematical theory of optimal processes: Математическая Теория Оптимальных Процессов. The Mathematical Theory of Optimal Processes. By L.S. Pontryagin, V.G. Boltyanskii, R.V. Gamkrelidze, and E.F. Mishchenko ... Translator: K.N. Trirogoff. Editor: L.W. Neustadt Lev Semenovich PONTRYAGIN, Vladimir Grigor'evich BOLTYANSKY, R. V. Gamkrelidze, E. F. Mishchenko, Lucien Wolf NEUSTADT, 1962 |
| the mathematical theory of optimal processes: Introduction to the Calculus of Variations and Control with Modern Applications John A. Burns, 2013-08-28 Introduction to the Calculus of Variations and Control with Modern Applications provides the fundamental background required to develop rigorous necessary conditions that are the starting points for theoretical and numerical approaches to modern variational calculus and control problems. The book also presents some classical sufficient conditions a |
| the mathematical theory of optimal processes: Classic Papers in Control Theory Richard Bellman, Robert Kalaba, 2017-11-15 Historically and technically important papers range from early work in mathematical control theory to studies in adaptive control processes. Contributors include J. C. Maxwell, H. Nyquist, H. W. Bode, other experts. 1964 edition. |
| the mathematical theory of optimal processes: An Introduction to the Mathematical Theory of Dynamic Materials Konstantin A. Lurie, 2007-05-15 This fascinating book is a treatise on real space-age materials. It is a mathematical treatment of a novel concept in material science that characterizes the properties of dynamic materials—that is, material substances whose properties are variable in space and time. Unlike conventional composites that are often found in nature, dynamic materials are mostly the products of modern technology developed to maintain the most effective control over dynamic processes. |
| the mathematical theory of optimal processes: Optimal Transport for Applied Mathematicians Filippo Santambrogio, 2015-10-17 This monograph presents a rigorous mathematical introduction to optimal transport as a variational problem, its use in modeling various phenomena, and its connections with partial differential equations. Its main goal is to provide the reader with the techniques necessary to understand the current research in optimal transport and the tools which are most useful for its applications. Full proofs are used to illustrate mathematical concepts and each chapter includes a section that discusses applications of optimal transport to various areas, such as economics, finance, potential games, image processing and fluid dynamics. Several topics are covered that have never been previously in books on this subject, such as the Knothe transport, the properties of functionals on measures, the Dacorogna-Moser flow, the formulation through minimal flows with prescribed divergence formulation, the case of the supremal cost, and the most classical numerical methods. Graduate students and researchers in both pure and applied mathematics interested in the problems and applications of optimal transport will find this to be an invaluable resource. |
| the mathematical theory of optimal processes: Fluctuations of Lévy Processes with Applications Andreas E. Kyprianou, 2014-01-09 Lévy processes are the natural continuous-time analogue of random walks and form a rich class of stochastic processes around which a robust mathematical theory exists. Their application appears in the theory of many areas of classical and modern stochastic processes including storage models, renewal processes, insurance risk models, optimal stopping problems, mathematical finance, continuous-state branching processes and positive self-similar Markov processes. This textbook is based on a series of graduate courses concerning the theory and application of Lévy processes from the perspective of their path fluctuations. Central to the presentation is the decomposition of paths in terms of excursions from the running maximum as well as an understanding of short- and long-term behaviour. The book aims to be mathematically rigorous while still providing an intuitive feel for underlying principles. The results and applications often focus on the case of Lévy processes with jumps in only one direction, for which recent theoretical advances have yielded a higher degree of mathematical tractability. The second edition additionally addresses recent developments in the potential analysis of subordinators, Wiener-Hopf theory, the theory of scale functions and their application to ruin theory, as well as including an extensive overview of the classical and modern theory of positive self-similar Markov processes. Each chapter has a comprehensive set of exercises. |
| the mathematical theory of optimal processes: Calculus of Variations and Optimal Control Theory Daniel Liberzon, 2011-12-19 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 |
| the mathematical theory of optimal processes: Optimal Control V. M. Alekseev, 2013-12-11 There is an ever-growing interest in control problems today, con nected with the urgent problems of the effective use of natural resources, manpower, materials, and technology. When referring to the most important achievements of science and technology in the 20th Century, one usually mentions the splitting of the atom, the exploration of space, and computer engineering. Achievements in control theory seem less spectacular when viewed against this background, but the applications of control theory are playing an important role in the development of modern civilization, and there is every reason to believe that this role will be even more signifi cant in the future. Wherever there is active human participation, the problem arises of finding the best, or optimal, means of control. The demands of economics and technology have given birth to optimization problems which, in turn, have created new branches of mathematics. In the Forties, the investigation of problems of economics gave rise to a new branch of mathematical analysis called linear and convex program ming. At that time, problems of controlling flying vehicles and technolog ical processes of complex structures became important. A mathematical theory was formulated in the mid-Fifties known as optimal control theory. Here the maximum principle of L. S. Pontryagin played a pivotal role. Op timal control theory synthesized the concepts and methods of investigation using the classical methods of the calculus of variations and the methods of contemporary mathematics, for which Soviet mathematicians made valuable contributions. |
| the mathematical theory of optimal processes: An Introduction to Optimal Control Problems in Life Sciences and Economics Sebastian Aniţa, Viorel Arnăutu, Vincenzo Capasso, 2011-05-05 Combining control theory and modeling, this textbook introduces and builds on methods for simulating and tackling concrete problems in a variety of applied sciences. Emphasizing learning by doing, the authors focus on examples and applications to real-world problems. An elementary presentation of advanced concepts, proofs to introduce new ideas, and carefully presented MATLAB® programs help foster an understanding of the basics, but also lead the way to new, independent research. With minimal prerequisites and exercises in each chapter, this work serves as an excellent textbook and reference for graduate and advanced undergraduate students, researchers, and practitioners in mathematics, physics, engineering, computer science, as well as biology, biotechnology, economics, and finance. |
| the mathematical theory of optimal processes: Mathematical Theory of Adaptive Control Vladimir G. Sragovich, 2006 The theory of adaptive control is concerned with construction of strategies so that the controlled system behaves in a desirable way, without assuming the complete knowledge of the system. The models considered in this comprehensive book are of Markovian type. Both partial observation and partial information cases are analyzed. While the book focuses on discrete time models, continuous time ones are considered in the final chapter. The book provides a novel perspective by summarizing results on adaptive control obtained in the Soviet Union, which are not well known in the West. Comments on the interplay between the Russian and Western methods are also included. |
| the mathematical theory of optimal processes: Practical Methods for Optimal Control and Estimation Using Nonlinear Programming John T. Betts, 2010-01-01 The book describes how sparse optimization methods can be combined with discretization techniques for differential-algebraic equations and used to solve optimal control and estimation problems. The interaction between optimization and integration is emphasized throughout the book. |
| the mathematical theory of optimal processes: Stochastic Processes and Filtering Theory Andrew H. Jazwinski, 2013-04-15 This unified treatment presents material previously available only in journals, and in terms accessible to engineering students. Although theory is emphasized, it discusses numerous practical applications as well. 1970 edition. |
| the mathematical theory of optimal processes: Proceedings , 1962 |
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Mathematics is a field of study that discovers and organizes methods, theories and theorems that are developed and proved for the needs …
Wolfram Mathematica: Modern Technical Computing
Mathematica is built to provide industrial-strength capabilities—with robust, efficient algorithms across …
Mathematics | Definition, History, & Importance | Brita…
Apr 30, 2025 · mathematics, the science of structure, order, and relation that has evolved from elemental practices of counting, measuring, and describing …
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