2002/12/04 by B. Langerock, Langerock, B.
Mathematics · #49Kxx #53Cxx #Differential Geometry (math.DG) #FOS: Mathematics #Optimization and Control (math.OC) #math.DG #math.OC #msc:49Kxx #msc:53Cxx
paper · pdf · doi:10.48550/arxiv.math/0212055
38p, accepted for publication in Acta Appl. Math
arxiv created 2002/12/04 · arxiv updated 2009/11/30
A coordinate-free proof of the Maximum Principle is provided in the specific case of an optimal control problem with fixed time. Our treatment heavily relies on a special notion of variation of curves that consist of a concatenation of integral curves of time-dependent vector fields with unit time component, and on the use of a concept of lift over a bundle map. We further derive necessary and sufficient conditions for the existence of so-called abnormal and strictly abnormal extremals.