Fast Assignment in Asset-Guarding Engagements using Function Approximation

TL;DR

This work tackles real-time missile allocation by solving an assignment problem that pairs $n$ pursuers with $n$ targets to minimize the maximum intercept time. The authors formulate a per-pair optimal control problem to obtain the intercept time, then replace the expensive computations with offline-trained neural-network function approximators that first classify feasibility and then predict minimum intercept times. The approximator constructs an online cost matrix $ ilde{C}$, enabling bottleneck assignment via $Z^*_{BAP}( ilde{C})$ with substantial speedups while maintaining high accuracy and robustness to variations in target guidance. Results show orders-of-magnitude reductions in cost-matrix computation time and high rates of matching bottleneck times to the true optimum, validating the approach for real-time, scalable asset-guarding engagements. The method paves the way for broader real-time combinatorial optimization in dynamic defense and emergency-response scenarios.

Abstract

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.

Figures (1)

• Figure 1: $3 \times 3$ Engagement with Maneuvering Targets. The dashed boxes represent the regions of possible initial conditions, with blue for the pursuers and red for targets. The blue dots labeled $P_i$ and the red dots labeled $T_i$ are the three pursuers and targets respectively at their starting locations. The arrows represent the initial velocities of the pursuers and targets. The red dashed lines are the targets' trajectories toward the asset, $A$, and the blue dashed lines are the pursuers' intercept trajectories, where the intercept points are the small blue dots.