Cooperative Aircraft Control for Minimum Radar Exposure

Abstract

Two aircraft exposed to illumination by a tracking radar are considered and the optimization problem of cooperatively steering them to a prespecified rendezvous point is addressed. First, the problem of a single aircraft exposed to illumination by a tracking radar is considered and the problem of determining in optimal planar trajectory connecting two prespecified points is addressed. The solution is shown to exist only if the angle phi(integral) formed by the lines connecting the radar to the two prespecified trajectory points, is less than 60degrees. In addition, expressions are given for the optimal path length, l*, and optimal cost. When the angle phi(integral) greater than or equal to 60degrees, an unconstrained optimal solution does not exist, and in order to render the optimization problem well posed, a path length constraint is imposed. Numerical optimization techniques are used to obtain optimal aircraft trajectories for the constrained case. Finally, the problem of isochronous rendezvous of the two aircraft is addressed using an optimization argument and the analytic results previously derived for a single aircraft trajectory.