Singularity theory approach to time averaged optimization
Authors: Davydov AA, Mena-Matos H
Publication Year: 2007
Reference: In Singularities in Geometry & Topology. Proceedings of the Trieste Summer School & Workshop, J-P. Brasselet, J. Damon, L.D.Trang, M. Oka (eds)
World Scientific Publishing Co. Pte. Ltd., Singapore pp. 598-628 [2007]
[ISBN 978-981-270-022-3]
Abstract
Using singularity theory tools we study the time averaged problem for control systems and profit densities on the circle. We show that the optimal strategy always can be selected within periodic cyclic motions and stationary strategies. When the problem depends additionally on a one dimensional parameter, we analyze generic transitions between these two types of strategies under change of the parameter and classify all generic singularities of the averaged profit as a function of the parameter.
KEYWORDS: Singularities; Averaged Optimization; Control Systems
KEYWORDS: Singularities; Averaged Optimization; Control Systems