Optimal Synthesis in a Model Problem with Two-Dimensional Control Lying in an Arbitrary Convex Set

Abstract

We consider a model nilpotent convex problem with two-dimensional control from an arbitrary convex set Ω. For the case in which Ω is a polygon, the problem is solved explicitly. For the case of an arbitrary set Ω, we completely describe the asymptotics of optimal trajectories and the geometric properties of the optimal synthesis.