Methods for searching degenerate extremal controls in linear control systems

In the class of control-linear optimal control problems, new forms of the maximum principle are proposed in the form of problems about a fixed point of control operators. Based on the new forms of the maximum principle, new definitions of degenerate extremal controls are given and their equivalence to the known concept of a degenerate extremal control is shown. The proposed new forms of the maximum principle allow constructing new iterative methods for searching for degenerate extremal controls with uniquely determined approximations of degenerate control values. Theorems on the convergence of iterative processes of the proposed methods are proved.