Optimization of right-hand sides of nonlocal boundary conditions in a controlled dynamical system

We study an optimal control problem described by a system of linear ordinary differential equations with boundary conditions containing point and integral values of the state variable. The controls occurring in the differential equations and the values of the right-hand sides of the nonlocal boundary conditions are determined in this problem. Necessary conditions for the existence and uniqueness of a solution of the boundary value problem and for the convexity of the objective functional, as well as necessary conditions for the optimality of the parameters to be optimized in the control problem, are studied. The formulas obtained for the gradient of the objective functional of the problem are used in the numerical solution of an illustrative problem. The results of numerical experiments are provided.