SINGULAR CONTROLS IN THE CLASSICAL SENSE FOR THE OPTIMAL CONTROL PROBLEM WITH NONLOCAL BOUNDARY CONDITIONS

We consider an optimal control problem in which the states of the system are determined by the control systems of ordinary differential equations with two-point boundary conditions. Admissible controls are selected from the class of bounded measurable functions with values in an open set. We calculate the increment of the functional formula of the second order. We use variations of the control to derive the necessary optimality conditions for singular controls in the classical sense.