Modifications of projection methods in bilinear optimal control problems

In the class of bilinear optimal control problems, methods of nonlocal improvement of control are considered based on non-standard formulas for the increment of the objective functional that do not contain the remainder of the expansions. Such formulas make it possible to construct conditions for improving control in the form of special fixed point problems of projection control operators. The considered form of control improvement conditions in the form of fixed point problems in the control space makes it possible to apply and modify the fixed point methods known in computational mathematics to find improving controls and construct relaxation control sequences. The conditions for improvement and optimality of control based on fixed point problems are analyzed. Iterative processes of searching for improving controls and constructing relaxation sequences of controls are constructed. The results of analytical and numerical comparison of the effectiveness of the proposed projection optimization methods with the known projection methods on test examples are presented.