Abstract
Let f and g be two smooth vector fields on a manifold M. Given a submanifold S of M, we study the local structure of time-optimal trajectories for the single-input control-affine system ?q = f(q) + ug(q) with the initial condition q(0) ? S. When the codimension s of S in M is small (s ? 4) and the system has a small codimension singularity at a point q0 ? S, we prove that all time-optimal trajectories contained in a sufficiently small neighborhood of q0 are finite concatenations of bang and singular arcs. The proof is based on an extension of the index theory to the case of general boundary conditions.
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