TY  - BOOK
AU  - Colonius,Fritz
ED  - SpringerLink (Online service)
TI  - Optimal Periodic Control
T2  - Lecture Notes in Mathematics,
SN  - 9783540391708
AV  - Q295 
U1  - 519 23
PY  - 1988///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg
KW  - Mathematics
KW  - Systems theory
KW  - Mathematical optimization
KW  - Systems Theory, Control
KW  - Calculus of Variations and Optimal Control; Optimization
N1  - 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
N2  - 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
UR  - http://dx.doi.org/10.1007/BFb0077931
ER  -