Extended Sufficient Conditions for Strong Minimality in the Bolza Problem: Applications to Space Trajectory Optimization

This paper expands the existing sufficiency results for the strong minimality of an extremal of the Bolza problem. We cover the case where the strict Legendre Clebsh conditions are not strictly verified. An efficient, easy to use, algorithm to prove minimality is provided. It can be used on solutions with bang-bang control and does not require any local controllability property. The interval where sufficiency is provided is maximized over a class of discontinuous Verification Functions determined solving a sequence of Riccati problems. This class of Verification Functions can be adapted to all kind of boundary conditions. The algorithms developed in this paper are applied to space trajectory extremals that exhibit bang-bang control.