Geometric Optimal Control: Theory, Methods and Examples by Urszula Ledzewicz (En

Description: Geometric Optimal Control by Urszula Ledzewicz, Heinz Schättler This book gives a comprehensive treatment of the fundamental necessary and sufficient conditions for optimality for finite-dimensional, deterministic, optimal control problems. FORMAT Hardcover LANGUAGE English CONDITION Brand New Publisher 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. Notes Comprehensive presentation of an up-to-date geometric approach to optimal control, both necessary and sufficient conditions, which has not been done in a book form beforeRigorous presentation, written in a easy tutorial style accessible to non-experts and advanced undergraduate and graduate studentsPalette of fully and in detail worked out, well illustrated, nontrivial examples which are only available in the research literature Back Cover 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 Sch Author Biography Urszula Ledzewicz is a Distinguished Research Professor in the Department of Mathematics and Statistics at Southern Illinois University. Heinz Schaettler is an Associate Professor at Washington University. Table of Contents The Calculus of Variations: A Historical Perspective.- The Pontryagin Maximum Principle: From Necessary Conditions to the Construction of an Optimal Solution.- Reachable Sets of Linear Time-Invariant Systems: From Convex Sets to the Bang-Bang Theorem.- The High-Order Maximum Principle: From Approximations of Reachable Sets to High-Order Necessary Conditions for Optimality.- The Method of Characteristics: A Geometric Approach to Sufficient Conditions for a Local Minimum.- Synthesis of Optimal Controlled Trajectories: FromLocal to Global Solutions.- Control-Affine Systems in Low Dimensions: From Small-Time Reachable Sets to Time-Optimal Syntheses.- References.- Index. Review From the reviews:"The monograph under review concerns finite-dimensional deterministic optimal control problems. … The main body of the book is divided into seven chapters. … The variety of fully solved examples that illustrate the theory makes this text a strong educational asset. The book is recommended as a comprehensive textbook for both advanced undergraduate and all levels of graduate courses on optimal control in mathematics and engineering." (Ovidiu Cârj, zbMATH, Vol. 1276, 2014)"The book presents a comprehensive treatment of both necessary and sufficient conditions for optimal control using geometric approach … . The book is of interest to senior and graduate students in engineering and mathematics, and scientists and engineers working in academic and industrial organizations. … The book is a valuable addition to some of the recent books on this ever-green field of Optimal Control … ." (D. Subbaram Naidu, Amazon.com, September, 2013)"Grown out of well-tested lecture notes, large parts of this volume are suitable as a comprehensive textbook at an advanced undergraduate or at the graduate level, either in mathematics or in engineering … . this most readable text provides a rich and versatile resource which is suitable as a textbook in various settings, is a valuable reference for theory, and which provides a very large collection of model examples that are analyzed completely using state-of-the-art methods." (Matthias Kawski, Mathematical Reviews, February, 2013)"Schättler (electrical and systems engineering, Washington Univ.) and Ledzewicz (mathematics and statistics, Southern Illinois Univ.) use a geometric approach to present the theory of optimal control. … authors have developed a general approach that can be applied to a wide variety of control problems. … This book may be of interest to graduate students and researchers working in this area. Summing Up: Recommended.Graduate students and researchers/faculty." (B. Borchers, Choice, Vol. 50 (5), January, 2013) Review Quote From the reviews: "Schttler (electrical and systems engineering, Washington Univ.) and Ledzewicz (mathematics and statistics, Southern Illinois Univ.) use a geometric approach to present the theory of optimal control. ... authors have developed a general approach that can be applied to a wide variety of control problems. ... This book may be of interest to graduate students and researchers working in this area. Summing Up: Recommended. Graduate students and researchers/faculty." (B. Borchers, Choice, Vol. 50 (5), January, 2013) "Grown out of well-tested lecture notes, large parts of this volume are suitable as a comprehensive textbook at an advanced undergraduate or at the graduate level, either in mathematics or in engineering ... . this most readable text provides a rich and versatile resource which is suitable as a textbook in various settings, is a valuable reference for theory, and which provides a very large collection of model examples that are analyzed completely using state-of-the-art methods." (Matthias Kawski, Mathematical Reviews, February, 2013) Feature Comprehensive presentation of an up-to-date geometric approach to optimal control, both necessary and sufficient conditions, which has not been done in a book form beforeRigorous presentation, written in a easy tutorial style accessible to non-experts and advanced undergraduate and graduate studentsPalette of fully and in detail worked out, well illustrated, nontrivial examples which are only available in the research literature Details ISBN1461438330 Author Heinz Schättler Publisher Springer-Verlag New York Inc. Series Interdisciplinary Applied Mathematics Year 2012 ISBN-10 1461438330 ISBN-13 9781461438335 Format Hardcover Imprint Springer-Verlag New York Inc. Place of Publication New York, NY Country of Publication United States DEWEY 515.642 Publication Date 2012-06-26 Edition Description 2012 Language English Media Book Series Number 38 Short Title GEOMETRIC OPTIMAL CONTROL Subtitle Theory, Methods and Examples Pages 640 DOI 10.1007/978-1-4614-3834-2 UK Release Date 2012-06-26 AU Release Date 2012-06-26 NZ Release Date 2012-06-26 US Release Date 2012-06-26 Illustrations XX, 640 p. Alternative 9781489986801 Audience Professional & Vocational We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:96283679;

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