Optimal periodic control
By: Fritz Colonius.
Series: Lecture notes in mathematics ;; 1313; Lecture notes in mathematics (Springer-Verlag) ;; 1313.
Publisher: Springer-Verlag
Published: 1988
Place of publication: Berlin; New York
Language: eng
Number of pages: 177
Subjects: Control theory.; Mathematical optimization.
Description: 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.
Notes: Bibliography: p. [167]-177.