### State estimation under communication constraints

Christoph Kawan

Abstract:
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.