  This letter considers assignment problems consisting of n pursuers attempting
to intercept n targets. We consider stationary targets as well as targets
maneuvering toward an asset. The assignment algorithm relies on an n x n cost
matrix where entry (i, j) is the minimum time for pursuer i to intercept target
j. Each entry of this matrix requires the solution of a nonlinear optimal
control problem. This subproblem is computationally intensive and hence the
computational cost of the assignment is dominated by the construction of the
cost matrix. We propose to use neural networks for function approximation of
the minimum time until intercept. The neural networks are trained offline, thus
allowing for real-time online construction of cost matrices. Moreover, the
function approximators have sufficient accuracy to obtain reasonable solutions
to the assignment problem. In most cases, the approximators achieve assignments
with optimal worst case intercept time. The proposed approach is demonstrated
on several examples with increasing numbers of pursuers and targets.
