The optimal control problem with integral boundary condition is considered. The sufficient condition is established for existence and uniqueness of the solution for a class of integral boundary value problems for fixed admissible controls. First-order necessary condition for optimality is obtained in the traditional form of the maximum principle. The second-order variations of the functional are calculated. Using the variations of the controls, various optimality conditions of second order are obtained.
"Maximum Principle in the Optimal Control Problems for Systems with Integral Boundary Conditions and Its Extension." Abstr. Appl. Anal. 2013 (SI18) 1 - 9, 2013. https://doi.org/10.1155/2013/946910