An approach to calculating degenerate extremal controls based on fixed point problems

In the class of optimal control problems linear with respect to the control, an approach to calculating degenerate controls that satisfy the maximum principle, is proposed. This approach is based on new optimality conditions in the form of fixed point problems that are equivalent to the well-known conditions of the maximum principle. New forms of conditions for the maximum principle make it possible to construct effective methods for searching for degenerate controls. The efficiency of the approach proposed is illustrated using model examples.