  We consider a rate control problem for an $N$-particle weakly interacting
finite state Markov process. The process models the state evolution of a large
collection of particles and allows for multiple particles to change state
simultaneously. Such models have been proposed for large communication systems
(e.g. ad hoc wireless networks) but are also suitable for other settings such
as chemical-reaction networks. An associated diffusion control problem is
presented and we show that the value function of the $N$-particle controlled
system converges to the value function of the limit diffusion control problem
as $N\to\infty$. The diffusion coefficient in the limit model is typically
degenerate, however under suitable conditions there is an equivalent
formulation in terms of a controlled diffusion with a uniformly non-degenerate
diffusion coefficient. Using this equivalence, we show that near optimal
continuous feedback controls exist for the diffusion control problem. We then
construct near asymptotically optimal control policies for the $N$-particle
system based on such continuous feedback controls. Results from some numerical
experiments are presented.
