*Article* **Defense against Adversarial Swarms with Parameter Uncertainty**

**Claire Walton 1,2,\*, Isaac Kaminer 3, Qi Gong 4, Abram H. Clark <sup>5</sup> and Theodoros Tsatsanifos <sup>3</sup>**


**Abstract:** This paper addresses the problem of optimal defense of a high-value unit (HVU) against a large-scale swarm attack. We discuss multiple models for intra-swarm cooperation strategies and provide a framework for combining these cooperative models with HVU tracking and adversarial interaction forces. We show that the problem of defending against a swarm attack can be cast in the framework of uncertain parameter optimal control. We discuss numerical solution methods, then derive a consistency result for the dual problem of this framework, providing a tool for verifying computational results. We also show that the dual conditions can be computed numerically, providing further computational utility. Finally, we apply these numerical results to derive optimal defender strategies against a 100-agent swarm attack.

**Keywords:** optimal control; parameter uncertainty; swarming
