Stochastic controllability and its role in network congestion control

Controllability and reachability concepts are developed for nonlinear stochastic systems motivated by a problem in network congestion control described by a Hidden Markov Model. These definitions are posed in terms of the capability to steer the state distribution towards certain target distributions, as measured by relative entropy. It is shown that this definition extends earlier approaches and, in the linear case, concurs with the usual rank and range conditions from deterministic analysis. For the network congestion control problem, these ideas are analyzed from two viewpoints: the capacity to steer the state distribution towards a specific target, reachability; the capacity to yield bottleneck node state distributions which maintain stochastic observability at the data source from acknowledgement packet and input rate data, controllability.