The Chattering Phenomenon on Finsler Manifolds with Polyhedral Norm

The well-known chattering phenomenon (i.e., a countable number of switches within an arbitrarily small time interval) typically arises in optimal control problems with drift. In this talk, we will present an example of a sub-Finsler manifold (i.e., a problem without drift) with a polyhedral structure where shortest paths exhibit chattering. We will also provide an explicit left-invariant sub-Finsler structure on a Carnot group of depth 5, in which geodesics contain chattering. Furthermore, we will propose a sufficient condition for Pontryagin Maximum Principle extremals of sub-Finsler problems to contain chattering.