Fuller singularities for generic control-affine systems with an even number of controls

TL;DR

This paper extends the understanding of singularities in time-optimal trajectories for control-affine systems to cases with an even number of controls, showing that such singularities are generically limited to finite order accumulations of Fuller points.

Contribution

It generalizes previous results from scalar controls to systems with an even number of controls, establishing bounds on the complexity of singularities.

Findings

Singularities are generically limited to finite order Fuller point accumulations.

The bounds depend only on the system's manifold dimension.

Results extend previous scalar control cases to multi-control systems.

Abstract

In this article we study how bad can be the singularities of a time-optimal trajectory of a generic control affine system. In the case where the control is scalar and belongs to a closed interval it was recently shown in [6] that singularities cannot be, generically, worse than finite order accumulations of Fuller points, with order of accumulation lower than a bound depending only on the dimension of the manifold where the system is set. We extend here such a result to the case where the control has an even number of scalar components and belongs to a closed ball.