A STUDY ON CONTROL AFFINE SYSTEMS WITH POSITIVE HOMOGENEOUS COST AND NO CONSTANT RANK OF DISTRIBUTION*
A STUDY ON CONTROL AFFINE SYSTEMS WITH POSITIVE HOMOGENEOUS COST AND NO CONSTANT RANK OF DISTRIBUTION*

Summary/Abstract: The paper deals with the study of a drift less control affine system with positive homogeneous cost of Randers type in the case of bracket generating distribution of no constant rank. We use the Pontryagin Maximum Principle in order to find the general solution. In the particular case of quadratic cost the optimal trajectories of the distributional system are the geodesics of the so called sub-Riemannian geometry.

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