On the solution of some optimal control problems for linear systems of functional-differential equations

The optimal control problem is considered for systems of linear functional-differential equations with the Letov-Kalman quality criterion. The proposed algorithm of its solution is based on the knowledge of the fundamental matrix of a system and on the construction of a functional space where the considered functional and boundary conditions can be represented as a scalar product. All this allows one to find a dependence of an optimal control on initial conditions and to pass to the minimization problem of a quadratic function with linear constraints. It is proved that this approach is also efficient for systems with perturbations of the white noise type, where the knowledge about the system's output is insufficient to recover its initial state, and also if an initial state is given and the right end of the trajectory belongs to a given set.