Two Extensions of Topological Feedback Entropy

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Topological feedback entropy (TFE) was introduced in 2004 to measure the intrinsic rate at which a continuous, fully observed, deterministic control system generates information for controlled set-invariance. In this paper, we generalise this notion in two directions, first to continuous, partially observed systems and then to discontinuous, fully observed systems. In each case, we show that the corresponding generalised TFE coincides with the the smallest feedback bit rate that allows a form of controlled invariance to be achieved.