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  • © 1988

Optimal Periodic Control

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

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Table of contents (9 chapters)

  1. Front Matter

    Pages I-VI
  2. Introduction

    • Fritz Colonius
    Pages 1-7
  3. Optimization theory

    • Fritz Colonius
    Pages 8-30
  4. Retarded functional differential equations

    • Fritz Colonius
    Pages 31-47
  5. Strong local minima

    • Fritz Colonius
    Pages 48-64
  6. Weak local minima

    • Fritz Colonius
    Pages 65-85
  7. Local relaxed minima

    • Fritz Colonius
    Pages 86-103
  8. Tests for local properness

    • Fritz Colonius
    Pages 104-128
  9. A scenario for local properness

    • 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.

Keywords

  • bifurcation
  • equation
  • function
  • optimization
  • proof
  • system

Bibliographic Information

  • Book Title: Optimal Periodic Control

  • Authors: Fritz Colonius

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0077931

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1988

  • Softcover ISBN: 978-3-540-19249-7Published: 11 May 1988

  • eBook ISBN: 978-3-540-39170-8Published: 15 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VI, 177

  • Topics: Systems Theory, Control , Calculus of Variations and Optimization

Buying options

eBook USD 29.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 39.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions