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25 Remote Warehouse Mathematics- Applied

Interdisciplinary Applied Mathematics #38: Geometric Optimal Control: Theory, Methods and Examples

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Synopses & Reviews

Publisher Comments:

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

Synopsis:

Here is a comprehensive review of the fundamental conditions for optimality for finite-dimensional, deterministic, optimal control problems. Includes worked examples ranging from minimum surfaces of revolution to cancer treatment for novel therapy approaches.

About the Author

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.

Product Details

ISBN:
9781461438335
Author:
Schaettler, Heinz
Publisher:
Springer
Author:
Ledzewicz, Urszula
Author:
Schättler, Heinz
Subject:
Calculus
Subject:
Lie bracket computations
Subject:
Pontryagin Maximum Principle
Subject:
Calculus of variations
Subject:
geometric optimal control
Subject:
reachable sets
Subject:
Calculus of Variations and Optimal Control; Optimization
Subject:
Control
Subject:
Differential geometry
Subject:
ordinary differential equations
Subject:
Appl.Mathematics/Computational Methods of Engineering
Subject:
Mathematics-Applied
Copyright:
Edition Description:
2012
Series:
Interdisciplinary Applied Mathematics
Series Volume:
38
Publication Date:
20120513
Binding:
HARDCOVER
Language:
English
Pages:
659
Dimensions:
235 x 155 mm

Related Subjects


Reference » Science Reference » Technology
Science and Mathematics » Mathematics » Applied
Science and Mathematics » Mathematics » Calculus » General
Science and Mathematics » Mathematics » Differential Equations
Science and Mathematics » Mathematics » Differential Geometry
Science and Mathematics » Mathematics » Numeric Analysis

Interdisciplinary Applied Mathematics #38: Geometric Optimal Control: Theory, Methods and Examples New Hardcover
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Product details 659 pages Springer - English 9781461438335 Reviews:
"Synopsis" by , Here is a comprehensive review of the fundamental conditions for optimality for finite-dimensional, deterministic, optimal control problems. Includes worked examples ranging from minimum surfaces of revolution to cancer treatment for novel therapy approaches.
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