© 1988

Optimal Periodic Control

  • Authors

Part of the Lecture Notes in Mathematics book series (LNM, volume 1313)

Table of contents

  1. Front Matter
    Pages I-VI
  2. Fritz Colonius
    Pages 1-7
  3. Fritz Colonius
    Pages 8-30
  4. Fritz Colonius
    Pages 31-47
  5. Fritz Colonius
    Pages 48-64
  6. Fritz Colonius
    Pages 65-85
  7. Fritz Colonius
    Pages 86-103
  8. Fritz Colonius
    Pages 104-128
  9. Fritz Colonius
    Pages 129-144
  10. Back Matter
    Pages 167-177

About this book


This research monograph deals with optimal periodic control problems for systems governed by ordinary and functional differential equations of retarded type. Particular attention is given to the problem of local properness, i.e. whether system performance can be improved by introducing periodic motions. Using either Ekeland's Variational Principle or optimization theory in Banach spaces, necessary optimality conditions are proved. In particular, complete proofs of second-order conditions are included and the result is used for various versions of the optimal periodic control problem. Furthermore a scenario for local properness (related to Hopf bifurcation) is drawn up, giving hints as to where to look for optimal periodic solutions. The book provides mathematically rigorous proofs for results which are potentially of importance in chemical engineering and aerospace engineering.


bifurcation equation function optimization proof system

Bibliographic information

  • Book Title Optimal Periodic Control
  • Authors Fritz Colonius
  • Series Title Lecture Notes in Mathematics
  • Series Abbreviated Title Lecture Notes in Mathematics
  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 1988
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Softcover ISBN 978-3-540-19249-7
  • eBook ISBN 978-3-540-39170-8
  • Series ISSN 0075-8434
  • Series E-ISSN 1617-9692
  • Edition Number 1
  • Number of Pages VI, 177
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Systems Theory, Control
    Calculus of Variations and Optimal Control; Optimization
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