On an inductive method for studying singular extremals

The singular extremal path is studied in a terminal optimal control problem. A method is proposed in which the combined effect of needle-like control variations at different times is studied. The notion of induced Hamiltonians is introduced and the mutuality principle is established for them. In terms of induced Hamiltonians the necessary optimality condition is formulated which is valid even in the case where the extremal path degenerates into second and higher order ones.