Optimal Periodic Control

by Fritz Colonius

Overview

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.

Product Details

ISBN-13:	9783540192497
Publisher:	Springer Berlin Heidelberg
Publication date:	06/13/1988
Series:	Lecture Notes in Mathematics , #1313
Edition description:	1988
Pages:	177
Product dimensions:	6.10(w) x 9.25(h) x 0.02(d)

Table of Contents

Optimization theory.- Retarded functional differential equations.- Strong local minima.- Weak local minima.- Local relaxed minima.- Tests for local properness.- A scenario for local properness.- Optimal periodic control of ordinary differential equations.