Choise of a version of descent in an optimal control problem with mixed constraints. A decompositional approach

A problem is discussed of optimal control with mixed constraints imposed on the control and state coordinates and conditions on the rightmost end of the path presented as inequalities. On a special class of variations consisting of an independent and a compensating part an estimate is true of the functional increment similar to the well-known L. I. Rozonoer's formula which includes only the independent component. The choice of the latter decomposes in that it reduces to solution of finite-dimensional problems for each time from the period. The compensation component is univalently determined once the independent one has been.