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Direct Methods in Control Problems

  • Peter Falb
Textbook

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Peter Falb
    Pages 11-18
  3. Peter Falb
    Pages 19-21
  4. Peter Falb
    Pages 57-78
  5. Peter Falb
    Pages 95-123
  6. Peter Falb
    Pages 125-147
  7. Peter Falb
    Pages 149-161
  8. Peter Falb
    Pages 163-171
  9. Peter Falb
    Pages 195-206
  10. Peter Falb
    Pages 207-210
  11. Back Matter
    Pages 211-314

About this book

Introduction

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.

Keywords

Lévy processes deterministic systems direct methods finite element methods gradient method integration methods representation methods stochastic systems systems and control

Authors and affiliations

  • Peter Falb
    • 1
  1. 1.Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, Cambridge, MA, USA and Division of Applied MathematicsBrown UniversityProvidenceUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-8176-4723-0
  • Copyright Information Springer Science+Business Media, LLC, part of Springer Nature 2019
  • Publisher Name Birkhäuser, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-8176-4722-3
  • Online ISBN 978-0-8176-4723-0
  • Buy this book on publisher's site