Geometric Optimal Control

Theory, Methods and Examples

  • Heinz Schättler
  • Urszula Ledzewicz

Part of the Interdisciplinary Applied Mathematics book series (IAM, volume 38)

Table of contents

About this book


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.


Lie bracket computations Pontryagin Maximum Principle calculus of variations geometric optimal control reachable sets

Authors and affiliations

  • Heinz Schättler
    • 1
  • Urszula Ledzewicz
    • 2
  1. 1., Electrical and Systems EngineeringWashington UniversitySaint LouisUSA
  2. 2., Mathematics and StatisticsSouthern Illinois University EdwardsvillEdwardsvilleUSA

Bibliographic information

  • DOI
  • Copyright Information Springer Science+Business Media, LLC 2012
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-3833-5
  • Online ISBN 978-1-4614-3834-2
  • Series Print ISSN 0939-6047
  • Buy this book on publisher's site