Modeling Large-Scale Adversarial Swarm Engagements using Optimal Control

We investigate the optimal control of large-scale autonomous systems under explicitly adversarial conditions, incorporating the probabilistic destruction of agents over time. In many such systems, adversarial interactions arise as different agents or groups compete against one another. A crucial yet often overlooked factor in existing theoretical and modeling frameworks is the random attrition of agents during operation. Effective modeling and control strategies must therefore account for both agent attrition and spatial dynamics. Given the inherently random nature of agent survival, directly solving this problem is challenging. To address this, we propose and evaluate three approximate numerical modeling approaches in which agent survival probabilities decrease deterministically over time based on their relative positions. We apply these schemes to a scenario where agents defend a high-value unit against an attacking swarm. Our results demonstrate that these models can effectively capture the dynamics of such interactions, provided that attrition and spatial positioning are tightly integrated. These findings are relevant to a broad range of adversarial autonomy scenarios where both agent positioning and survival probabilities play a critical role.