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A new approach to solving optimal control problems with terminal and phase constraints is proposed on the basis of constructing and solving a system of conditions for improving admissible control in the form of the fixed point problem for a constructed control operator. This form makes it possible to apply the developed theory and fixed-point methods for the effective search of admissible improving controls. To construct these conditions, we apply the transition to the auxiliary problem of optimizing a regular Lagrange functional without constraints with mixed control functions and parameters. Approbation and comparative analysis of the effectiveness of the proposed approach of fixed points on model and test examples are carried out.

The Method of Non-Local Control Improvement in Optimal Control Problems with Constraints