Optimization methods for bilinear control systems based on fixed point problems

In the class of bilinear optimal control problems, conditions of optimality and control improvement in the form of special fixed-point problems on a set of admissible controls are considered. The obtained conditions of optimality and control improvement in the form of fixed-point problems make it possible to apply and modify the technique of the fixed-point theory and methods known in computational mathematics to search for extremal and improving controls. Iterative methods for the search for extremal and improving controls are constructed and analyzed. The efficiency of the proposed optimization methods are compared with the known methods.