### Minimal data rates and entropy for control problems

Christoph Kawan

Abstract:
In the theory of networked control systems, the assumption of
classical control theory that information can be transmitted within
control loops instantaneously, lossless, and with arbitrary precision
is no longer satisfied. This raises the question about the smallest
possible information rate above which a given control task can be
solved. Though networked control systems can have a complicated
topology, consisting of multiple sensors, controllers, and actuators,
a first step towards understanding the problem of minimal data rates
is to analyze the simplest possible network topology, consisting of
one controller and one dynamical system connected by a digital channel
with a certain rate in bits per unit time. In this setting, the notion
of feedback entropy or invariance entropy provides a measure for the
minimal data rate associated with the control objective of rendering a
subset of the state space invariant. In my talk, I will explain this
concept and present results which show that the feedback/invariance
entropy can be estimated in terms of dynamical quantities of the
control system such as Lyapunov exponents, volume growth and escape
rates.