Necessary Optimality Condition for the Singular Controls in an Optimal Control Problem with Nonlocal Conditions

Abstract

In the paper we continue investigation of the problem considered in our earlier works.
Here we consider optimal control problem for the ordinary differential equation with integral
boundary conditions that generalizes the Cauchy problem and firstly investigate the case when
Pontryagin’s maximum principle degenerate. Second order optimality conditions are derived for
the considered problem.