Introduction to Invariance Entropy

Abstract

This chapter gives an introduction to the concept of invariance entropy. For topological time-invariant systems, different notions of invariance entropy are defined and investigated. We show that invariance entropy shares several elementary properties with the entropy notions in the classical theory of dynamical systems, that is, with metric and topological entropy. Section 2.3 provides a first nontrivial example for a system which allows for an explicit computation of the associated invariance entropies. The last two sections are concerned with the relations between invariance entropy and minimal data rates. In particular, the relation to the topological feedback entropy introduced by Nair et al. (IEEE Trans. Autom. Control 49(9):1585–1597, 2004) is investigated in Sect. 2.4.