Topological feedback entropy for nonlinear Stabilization
Nair GN., Evans RJ., Mareels IMY., Moran W.
In this paper, it is shown that, the problem of communication-limited Stabilization is related to the concept of topological entropy, introduced by Adler et. al. as a measure of the information rate of a continuous map on a compact topological space. Using open covers, the notion of topological feedback entropy (TFE) is defined and proposed as a measure of the inherent rate at which a map on a noncompaet topological space with inputs generates stability information. It is then proven that a topological dynamical plant can be stabilized into a compact set if and only if the data rate in the feedback loop exceeds the TFE of the plant on the set.