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For control systems in discrete time, this paper considers metric (i.e., measure-theoretic) invariance entropy for a subset Q of the state space with respect to a conditionally invariant measure. The main result shows that this entropy is already determined by certain subsets of Q which are characterized by controllability properties.
The purpose of this tutorial paper is to explain and to survey a number of concepts and results for deterministic control systems centering on the problem to determine the “information” needed for performing control tasks. Entropy theory of dynamical systems provides a guideline in the sense that the developments for control systems are seen, sometimes in analogy and sometimes in contrast, to those...
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