Methods of numerical solution of optimal control problems based on the Pontryagin maximum principle

In this paper, we study optimal control problems whose behavior is described by second-order differential equations with nonlocal Bitsadze–Samarski boundary conditions. Necessary conditions of optimality are obtained in terms of the maximum principle; adjoint equations are constructed in the differential and integral form. Necessary and sufficient optimality conditions are obtained for a linear problem, a difference scheme is constructed and examined, and a numerical algorithm is proposed.