Authors:
- Fills a gap in literature, covering direct methods applications in the control and systems context; takes into account recent significant advances in computing; most other books cover indirect methods
- New material is presented, in particular, a treatment of representation methods for stochastic systems involving Lévy processes
- Varied examples throughout are a valuable pedagogical tool and of independent interest to researchers and students
- For a broad audience of graduate students, researchers, applied mathematicians, and control engineers
- May be used as a textbook for a graduate course or seminar on direct methods in control
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Table of contents (15 chapters)
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Front Matter
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Back Matter
About this book
The primary focus of this book is on explicating the direct method approach. Historically, direct methods have not been fully exploited in control problems. The key is constructing convergent minimizing families. Integration methods (for example the gradient method) and representation methods (such as the Ritz-Galerkin and Finite Element methods) are examined in this text in an abstract (with concrete examples) functional analytic way. The aim is to consider direct methods from a unified general point of view and to provide a stimulus for future research. Explicitly, implicitly and by example, potential areas of research interest are indicated.
The book is a suitable reference for graduate students, researchers, applied mathematicians, and control engineers. Some of the material is of independent mathematical interest. The work may be used as a text for a graduate course or seminar on direct methods in control. A degree of mathematical sophistication and some knowledge of control theory is required.
Reviews
“This is clearly a book aimed at specialists in control theory. It is more a monograph … .” (Bill Satzer, MAA Reviews, November 28, 2021)
“This book offers a useful reading and provides interesting classroom material on the theory of finite-element indirect methods for optimal control problems.” (Fernando Lobo Pereira, Mathematical Reviews, July, 2021)
“The book will become a valuable reference for researchers, engineers and students in the field of mathematics, management science, operations research, optimal control science and economics.” (Savin Treanta, zbMATH 1444.93002, 2020)
Authors and Affiliations
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Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, Cambridge, MA, USA and Division of Applied Mathematics, Brown University, Providence, USA
Peter Falb
About the author
Bibliographic Information
Book Title: Direct Methods in Control Problems
Authors: Peter Falb
DOI: https://doi.org/10.1007/978-0-8176-4723-0
Publisher: Birkhäuser New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media, LLC, part of Springer Nature 2019
Hardcover ISBN: 978-0-8176-4722-3
eBook ISBN: 978-0-8176-4723-0
Edition Number: 1
Number of Pages: XIII, 311
Number of Illustrations: 14 b/w illustrations
Topics: Systems Theory, Control, Control, Robotics, Mechatronics, Calculus of Variations and Optimal Control; Optimization, Approximations and Expansions, Probability Theory and Stochastic Processes, Computational Mathematics and Numerical Analysis