Lecture Notes in Mathematics

Colonius, Fritz

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.

Details

Published by: Springer

Publication Date: 1988-05-11

Format: Paperback

ISBN-13: 9783540192497

DOI: 10.1007/BFb0077931

Dimensions: 235cm x155cm

Pages: 177