Stabilization of networked systems under computational power constraints

The paper considers stabilization under communication errors and limited data rate by means of realistic controllers with bounded (as time progresses) computational powers. Discrete-time partially observed noisy linear systems are studied for which the sensor signals are communicated to the controller over a finite capacity stochastic digital link. Addressed is 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 domain where stabilization can be ensured by a coder and decoder with bounded expected computational powers is given by the ordinary Shannon capacity of the noisy channel.