State estimation under communication constraints
Christoph Kawan

Networked control systems challenge the standard assumption of control 
theory that controllers and actuators have access to state information 
of infinite precision. For the accomplishment of many control tasks it 
is crucial that the controller can estimate the state with a given 
precision. In the simplest setup, one dynamical system connected via a 
digital channel of finite capacity to an estimator, the smallest channel 
capacity above which a state estimation of arbitrarily small but finite 
precision is possible is related to the entropy of the dynamical system. 
In a purely deterministic setup, the critical capacity is completely 
characterized by the topological entropy. In a stochastic framework, 
depending on the formulation of the problem, the metric or topological 
entropy of an associated random dynamical system provides a lower bound 
on the critical capacity. However, the situation in this setting is more 
delicate. If the noise is additive, for instance, the receiver is able 
to recover also the noise process from the state information with an 
accuracy of the same order. Hence, the entropy of the shift dynamical 
system on the space of noise realizations provides another, usually 
infinite, lower bound. A complete solution of the problem in this case 
is not yet available. This talk provides a survey of known results and 
open problems.