Guarding a Target Area from a Heterogeneous Group of Cooperative Attackers

In this paper, we investigate a multi-agent target guarding problem in which a single defender seeks to capture multiple attackers aiming to reach a high-value target area. In contrast to previous studies, the attackers herein are assumed to be heterogeneous in the sense that they have not only different speeds but also different weights representing their respective degrees of importance (e.g., the amount of allocated resources). The objective of the attacker team is to jointly minimize the weighted sum of their final levels of proximity to the target area, whereas the defender aims to maximize the same value. Using geometric arguments, we construct candidate equilibrium control policies that require the solution of a (possibly non-convex) optimization problem. Despite its nonconvex nature, we establish a sufficient condition for this problem to admit a unique local minimum that is also global. Subsequently, we validate the optimality of the candidate control policies using parametric optimization techniques. Lastly, we provide numerical examples to illustrate how cooperative behaviors emerge within the attacker team due to their heterogeneity.