Overview
- Class-tested in mathematical institutions throughout the world
- Includes a stand-alone review of classical optimal control theory
- Presents a new version of the maximum principle for the construction of optimal control strategies for the class of uncertain systems given by a system of ordinary differential equations with unknown parameters from a given set that corresponds to different scenarios of possible dynamics
- Real-world applications to areas such as production planning and reinsurance-dividend management
- Applications of obtained results from dynamic programming derivations to multi-model sliding mode control and multi-model differential games
- Includes supplementary material: sn.pub/extras
Part of the book series: Systems & Control: Foundations & Applications (SCFA)
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Table of contents (17 chapters)
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Front Matter
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Topics of Classical Optimal Control
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Front Matter
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Tent Method
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Front Matter
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Robust Maximum Principle for Deterministic Systems
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Front Matter
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Robust Maximum Principle for Stochastic Systems
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Front Matter
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Keywords
- Banach spaces
- Feynman–Kac formula
- Kuhn–Tucker Theorem
- Lagrange principle
- Riccati differential equation
- deterministic systems
- dynamic programming methods
- linear quadratic control
- maximum robust principle
- min-max problem
- optimal control theory
- robust maximum principle
- stochastic systems
- tent method
- viscosity solutions
About this book
Both refining and extending previous publications by the authors, the material in this monograph has been class-tested in mathematical institutions throughout the world. Covering some of the key areas of optimal control theory (OCT)—a rapidly expanding field that has developed to analyze the optimal behavior of a constrained process over time—the authors use new methods to set out a version of OCT’s more refined ‘maximum principle’ designed to solve the problem of constructing optimal control strategies for uncertain systems where some parameters are unknown. Known as a ‘min-max’ problem, this type of difficulty occurs frequently when dealing with finite uncertain sets.
The text begins with a standalone section that reviews classical optimal control theory. Moving on to examine the tent method in detail, the book then presents its core material, which is a more robust maximum principle for both deterministic and stochastic systems. The results obtained have applications in production planning, reinsurance-dividend management, multi-model sliding mode control, and multi-model differential games.
Using powerful new tools in optimal control theory, this book explores material that will be of great interest to post-graduate students, researchers, and practitioners in applied mathematics and engineering, particularly in the area of systems and control.
Reviews
From the reviews:
“This book is a useful and positive contribution to the literature of optimal control theory. … The book covers a rather expansive collection of topics, individual topics are usually well motivated, and most chapters have concluding and, on occasion, historical remarks to provide useful perspective to the reader. … more suitable as a reference for researchers … .” (Kevin A. Grasse, Mathematical Reviews, September, 2013)
“This good structured and really clearly written book is worth reading both for readers interested in theory and applications of optimal control. For theory, since robustness embraces dependencies and sensitivities with respect to deterministic or stochastic uncertainties, and for applications, since robustness of a method is responsible for a good use of numerical results. … The special technique specific for stochastic calculus is fully used in the last section of the book and supports the recommendation that it is a pleasure to read this book.” (Alfred Göpfert, Zentralblatt MATH, Vol. 1239, 2012)Authors and Affiliations
Bibliographic Information
Book Title: The Robust Maximum Principle
Book Subtitle: Theory and Applications
Authors: Vladimir G. Boltyanski, Alexander S. Poznyak
Series Title: Systems & Control: Foundations & Applications
DOI: https://doi.org/10.1007/978-0-8176-8152-4
Publisher: Birkhäuser Boston, MA
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media, LLC 2012
Hardcover ISBN: 978-0-8176-8151-7Published: 05 November 2011
eBook ISBN: 978-0-8176-8152-4Published: 06 November 2011
Series ISSN: 2324-9749
Series E-ISSN: 2324-9757
Edition Number: 1
Number of Pages: XXII, 432
Number of Illustrations: 36 b/w illustrations
Topics: Systems Theory, Control, Control and Systems Theory, Calculus of Variations and Optimal Control; Optimization, Vibration, Dynamical Systems, Control, Mathematical and Computational Engineering