State-local optimality of a bang-bang trajectory: a Hamiltonian approach

We give a sufficient condition for a bang-bang extremal to be a strong local optimizer for the minimum time problem with fixed endpoints. We underline that the conditions imply that the optimum is local with respect to the state and not necessarily to the final time. Moreover it is given through a finite-dimensional minimization problem, hence is suited for numerical verification. A geometric interpretation through the projection of the Hamiltonian flow on the state-space is also given.