Abstract
In this paper, we study the solvability of optimal singular control problems by making the most of the generalized Legendre-Clebsch condition for the optimality of the singular control. Using the Hamiltonian expression of Maximum Principle and the variational formula of Rozonoér, we discuss the local attainability along the singular trajectory and the conditions of invariance, in other words, the local strong attainability distribution. It seems possible to find out solvable cases of the optimal singular control problems left unsolved since the sixties of the 20th century.
