Geometric aspects of the Maximum Principle and lifts over a bundle map

Details Geometric aspects of the Maximum Principle and lifts over a bundle map Geometric aspects of the Maximum Principle and lifts over a bundle map

2002-12-04

arxiv.org/abs/math/0212055v1

Mathematics

Differential Geometry

38p, accepted for publication in Acta Appl. Math

Scientific paper

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.

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