Proceedings of the International Conference on the Calculus of Variations and Related Topics,
Haifa, March 1998
Abstract
For singular extremals in the above class of problems conditions of a Pontryagin minimum include
a new pointwise condition, i.e. a condition of Legendre type. It involves not only the second,
but also the third variation of Lagrange function, and requires to solve a nontrivial auxiliary
optimal control problem. Some cases of its exact solution are presented.
Key words:
singular extremal, weak and Pontryagin minimum, quadratic order of estimation,
necessary and sufficient conditions, second and third variations of Lagrange function.