Extended Sufficient Conditions of Strong Minimality for the Bolza Problem with Bang Bang Controls. Applications to Space Trajectory Optimization

Abstract

This paper presents extended sufficiency results for the local minimality of an extremal of the Bolza problem. These results provide an essential improvement in the state of the art because they are applicable for bang–bang control without requiring the strict Legendre and controllability conditions. Extended sufficient conditions subsume the classic Jacobi conjugate point sufficiency conditions. Necessary conditions of the second order allow to exclude the minimality when sufficiency is not verified. All these results are applicable to space trajectory optimization both in low thrust and in impulsive transfer.