Barrier trajectories of a realistic missile/traget pursuit-evasion game

Abstract

This paper presents barrier trajectories of a pursuit-evasion game formulation of a missile/target encounter. Two practically important observations are made:

• - For sufficiently long flight time the missile climbs up to 20 km altitude or more to exploit the small drag for enlarging its range. Accordingly, the optimal flight path angle at launch time is extremely high (up to 70°).

• - The optimal target evasion maneuver generally ends on the dynamic pressure constraint, which prevents the aircraft from diving.

The multiple shooting algorithm turns out to be a useful tool for solving differential games:

• - For the solution of (one sided) optimal control problems there are competing nonlinear programming algorithms. This is not true in the area of differential games.

• - The solutions of the typically ill-conditioned multipoint boundary value problems are highly accurate and provide full information about the "switching structure" of the optimal control.

• - The multiple shooting technique and the associated software package is an excellent tool to generate a series of solutions for continuously varying boundary conditions ("continuation" or "homotopy") and to demarcate the validity domains of switching structures.

The reduced vehicle model (flight path angle as control) permits a two dimensional tabular representation of the maximum firing range for each initial state of the missile. This property could be preserved in the complete model (flight path angle as state variable) if initial elevation was treated as a free parameter also subject to optimization.

Results are presented for a missile, which is guided optimally in the sense of differential game theory. To quantify the loss of firing range for a conventionally guided missilc would be an interesting task.