Application of the envelope method to synthesis of control in the differential game “pursuit-evasion”

The report is devoted to the applications of the envelope method to the synthesis of control in the differential game "pursuit-evasion". It is proved that optimal trajectories can be represented as envelopes of a parametric family of singular curves, called instantaneous solutions within this approach, and that control can be found on this family. It is shown that, in the general case, the synthesized game control law will contain the maximum permissible control values, current values of phase coordinates, parameters of tangents and their derivatives.