Optimization via characteristic functions of cones

As Finsler metrics generalize Riemannian metrics, so one can generalize Lorentzian metrics to the consideration of manifolds equipped with a cone field and an appropriately smooth function F on the tangent bundle such that F restricted to each tangent space yields a so-called “length function” for the cone assigned to that point. This provides a type of quantification of a typical situation arising in nonsmooth analysis and and control. As in Lorentzian geometry, one considers “forward” curves in the manifold which are length maximizing. In this paper we consider how the methods of optimal control can be applied to the study of these curves.