On sufficient optimality conditions for a singular extremal

摘要

The paper is a first step in proving second order sufficient optimality conditions for singular extremals. The conditions include regularity conditions on the Hamiltonian associated to the problem and the absence of conjugate times. The definition of conjugate time is given by means of a suitable linear Hamiltonian system. In a forthcoming paper it is proved that the linear Hamiltonian system is the one associated to the second variation of the problem.