Advertisement

© 1994

Theory of Chattering Control

with applications to Astronautics, Robotics, Economics, and Engineering

Book

Part of the Systems & Control: Foundations & Applications book series (SCFA)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Michail I. Zelikin, Vladimir Borisov
    Pages 1-18
  3. Michail I. Zelikin, Vladimir Borisov
    Pages 19-37
  4. Michail I. Zelikin, Vladimir Borisov
    Pages 38-84
  5. Michail I. Zelikin, Vladimir Borisov
    Pages 85-104
  6. Michail I. Zelikin, Vladimir Borisov
    Pages 105-166
  7. Michail I. Zelikin, Vladimir Borisov
    Pages 167-215
  8. Michail I. Zelikin, Vladimir Borisov
    Pages 217-233
  9. Michail I. Zelikin, Vladimir Borisov
    Pages 235-235
  10. Back Matter
    Pages 236-244

About this book

Introduction

The common experience in solving control problems shows that optimal control as a function of time proves to be piecewise analytic, having a finite number of jumps (called switches) on any finite-time interval. Meanwhile there exists an old example proposed by A.T. Fuller [1961) in which optimal control has an infinite number of switches on a finite-time interval. This phenomenon is called chattering. It has become increasingly clear that chattering is widespread. This book is devoted to its exploration. Chattering obstructs the direct use of Pontryagin's maximum principle because of the lack of a nonzero-length interval with a continuous control function. That is why the common experience appears misleading. It is the hidden symmetry of Fuller's problem that allows the explicit solution. Namely, there exists a one-parameter group which respects the optimal trajectories of the problem. When published in 1961, Fuller's example incited curiosity, but it was considered only "interesting" and soon was forgotten. The second wave of attention to chattering was raised about 12 years later when several other examples with optimal chattering trajectories were 1 found. All these examples were two-dimensional with the one-parameter group of symmetries.

Keywords

Finite Lagrangian manifolds chattering control function optimal control theory of optimal control

Authors and affiliations

  1. 1.Department of MathematicsMoscow State UniversityMoscowRussia
  2. 2.Department of MathematicsMoscow Technological InstituteMoscowRussia

Bibliographic information

  • Book Title Theory of Chattering Control
  • Book Subtitle with applications to Astronautics, Robotics, Economics, and Engineering
  • Authors Michail I. Zelikin
    Vladimir F. Borisov
  • Series Title Systems & Control: Foundations & Applications
  • DOI https://doi.org/10.1007/978-1-4612-2702-1
  • Copyright Information Birkhäuser Boston 1994
  • Publisher Name Birkhäuser Boston
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-0-8176-3618-0
  • Softcover ISBN 978-1-4612-7634-0
  • eBook ISBN 978-1-4612-2702-1
  • Edition Number 1
  • Number of Pages XVI, 244
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Calculus of Variations and Optimal Control; Optimization
    Systems Theory, Control
  • Buy this book on publisher's site

Reviews

"...a rich source of information."
— Mathematical Reviews

"This book is an excellent introduction to and survey of chattering optimal controls."
— SIAM Review

"The book is an interesting and modern study of some problems in control theory in the language of differential geometry."
— Zentralblatt Math