  We theoretically and numerically study the problem of optimal control of
large-scale autonomous systems under explicitly adversarial conditions,
including probabilistic destruction of agents during the simulation.
Large-scale autonomous systems often include an adversarial component, where
different agents or groups of agents explicitly compete with one another. An
important component of these systems that is not included in current theory or
modeling frameworks is random destruction of agents in time. In this case, the
modeling and optimal control framework should consider the attrition of agents
as well as their position. We propose 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. In particular, we apply these schemes to the case of
agents defending a high-value unit from an attacking swarm. We show that these
models can be successfully used to model this situation, provided that
attrition and spatial dynamics are coupled. Our results have relevance to an
entire class of adversarial autonomy situations, where the positions of agents
and their survival probabilities are both important.
