On one approach to optimization of the controlled systems with restrictions on the basis of a fixed point problem

In the article we consider a new approach to solving optimal control problems with constraints based on construction and solution of a system of conditions for improving control in the form of a fixed point problem for control operator. To construct these conditions we apply the transition to an auxiliary problem without restrictions and with a regular Lagrange functional. Iterative algorithms for successive control improvement are constructed on the basis of a fixed point problem. We illustrate this approach by an example.