  This paper introduces a probabilistic guidance approach for the
swarm-to-swarm engagement problem. The idea is based on driving the controlled
swarm towards an adversary swarm, where the adversary swarm aims to converge to
a stationary distribution that corresponds to a defended base location. The
probabilistic approach is based on designing a Markov chain for the
distribution of the swarm to converge a stationary distribution. This approach
is decentralized, so each agent can propagate its position independently of
other agents. Our main contribution is the formulation of the swarm-to-swarm
engagement as an optimization problem where the population of each swarm decays
with each engagement and determining a desired distribution for the controlled
swarm to converge time-varying distribution and eliminate agents of the
adversary swarm until adversary swarm enters the defended base location. We
demonstrate the validity of proposed approach on several swarm engagement
scenarios.
