A Model for Perimeter-Defense Problems with Heterogeneous Teams

We develop a model of the multi-agent perimeter-defense game to calculate how an adaptive defense should be organized. This model is inspired by the human immune system and captures settings such as heterogeneous teams, limited resource allocations, partial observability of the attacking side, and decentralization. An optimal defense, that minimizes the harm under constraints of the energy spent to maintain a large and diverse repertoire, must maintain coverage of the perimeter from a diverse attacker population. The model characterizes how a defense might take advantage of its ability to respond strongly to attackers of the same type but weakly to attackers of diverse types to minimize the number of diverse defenders and while reducing harm. We first study the model from a steady-state perimeter-defense perspective and then extend it to mobile defenders and evolving attacker distributions. The optimal defender distribution is supported on a discrete set and similarly a Kalman filter obtaining local information is able to track a discrete, sometimes unknown, attacker distribution. Simulation experiments are performed to study the efficacy of the model under different constraints.