Data rate limitations for observability of nonlinear systems

The paper deals with observation of nonlinear and deterministic, though maybe chaotic, discrete-time systems via finite capacity communication channels. We consider various types of observability, and offer new tractable analytical techniques for both upper and lower estimation of the threshold that separates data rates for which reliable state observation is and is not possible, respectively. The main results are illustrated via their application to two celebrated samples of chaotic systems associated with the logistic and Lozi maps, respectively. In these cases, the thresholds attributed to some of the considered notions of observability are found in a closed form; they are shown to continuously depend on the parameters of the Lozi system.