Seminar Details
2013-09-03 (14.00) : Minimal Data Rates and Entropy for Control Problems
At Euler building
Organized by Mathematical Engineering
Speaker :
Kawan, Christoph
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 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 the foundations of a theory which aims at finding
expressions for feedback entropy in terms of dynamical quantities such as Lyapunov exponents.