Title:  Control and communication: an overview

            Jean Charles Delvenne
   Center for the Mathematics of Information
       California Institute of Technology 

ABSTRACT:  Telesurgery, a robot on Mars or a self-driving car: more and more
systems are nowadays controlled through various communication channels.
Hence we need to understand how control theory and information theory relate
to each other. 

A typical mathematical setup is the following: we want to force the state of
an unstable system to remain bounded. At every time we observe the state
through an imperfect communication channel and we must take the best
decision on how to act on the system, given this partial information.

A great amount of research has been produced in that direction in the recent
years, and several frameworks have been studied, differing mainly on the
definition of 'system'  (e.g., deterministic or stochastic) ,  'channel'
(e.g., noiseless or noisy) and 'best decision'.

In this talk, we review some of these different frameworks, the main results
and typical methods of proof. For instance, we will see that the rate needed
to stabilize a system must be greater than the logarithm of the unstable
eigenvalues of the system.