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Optimal Periodic Control

  • Book
  • © 1988

Overview

Authors:
  1. Fritz Colonius
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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
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  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. Optimal periodic control of ordinary differential equations

    • Fritz Colonius
    Pages 145-166

  11. Back Matter

    Pages 167-177
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Keywords

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.

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