Modeling Large-Scale Adversarial Swarm Engagements using Optimal Control

TL;DR

This work proposes and test three numerical modeling schemes, where survival probabilities of all agents are smoothly and continuously decreased in time, based on the relative positions of all Agents during the simulation, and shows that these models can be successfully used to model the case of agents defending a high-value unit from an attacking swarm.

Abstract

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.

Figures (8)

• Figure 1: Normal Distribution Function $\Phi$ used to define the attrition rate functions $d_{ik}^{\rm att}$ and $d_{ki}^{\rm def}$.
• Figure 2: Unoptimized (a) and optimized (b) defender trajectories are shown for a confrontation of 100 attacking swarm agents with a HVU protection force of 25 defenders with superior weapons. The optimized trajectories defend the HVU more effectively, as shown in (c).
• Figure 3: Comparison of the performance of the 3 proposed models for optimization with the Monte Carlo simulation model in a scenario of 2066 attackers and 200 defenders
• Figure 4: Optimized cost versus number of defenders for all three proposed models for optimization against a swarm of 50 assets
• Figure 5: Analysis of optimization results at Data Points A1. Insufficient number of defenders for HVU protection

Theorems & Definitions (3)

• Remark 1
• Remark 2
• Remark 3