The Problem of Stabilization of Networked Systems under Computational Power Constraints

The paper addresses stabilization under communication errors and limited data rate by means of controllers with bounded (as time progresses) computational powers. Discrete-time partially observed linear systems perturbed by stochastic additive disturbances are studied. The sensor signals are communicated to the controller over a noisy finite capacity link modeled as a stochastic discrete memoryless channel (DMC). We study stabilization in probability. It is shown that stability cannot typically be achieved by means of a finite memory decoder-controller so far as the boundary of the corresponding stabilizability domain is given by the zero-error capacity of the channel, which is typically zero. At the same time, stability can be achieved with keeping the expected values of the consumed computational resources bounded: the boundary of the relevant stabilizability domain is given by the ordinary Shannon capacity of the noisy channel, which is typically nonzero.