Stabilization of stochastic linear plants via limited capacity stochastic communication channels

Abstract

The paper considers a stabilization problem involving communication errors and limited data rate. Discrete-time partially observed noisy linear systems are studied. Unlike the classic problem setup, the sensor signals are communicated to the controller over a finite capacity stochastic digital link. Addressed is stabilization in probability by means of realistic controllers that are not only non-anticipating but also consume uniformly bounded (as time progresses) computational complexity and memory per unit time. It is shown that the border of the stabilizability domain is given by the classic Shannon capacity of the channel. A stabilizing controller is explicitly constructed.