Optimal Engagement for an Attacker with Limited Weapon Energy

We examine a real-time target engagement scenario in which a mobile attacker engages a fortified, static target and then retreats to a safety region. The mobile attacker possesses limited weapon energy (or ammunition) and must determine when to employ its limited resources to achieve maximum effect. Simultaneously, the hardened target inflicts an integral cost on the attacker over the course of the engagement. This instantaneous damage dealt by both agents is a function of the relative state with regions of high damage and low damage. We solve for the optimal attacker engagement strategy, which divides the state space into regions of qualitatively different behaviors, with different combinations and sequencing of holding fire, opening fire, approaching the target, and retreating. These regions are separated by several unique singular surfaces and constrained arcs. Furthermore, the global solution produces “kiting behaviors” which are often found in video games as well as traditional combat strategies.