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System Identification Entropy for Chen-Fliess Series and Their Interconnections

The notion of system identification entropy is defined for the class of analytic nonlinear input-output systems having Chen-Fliess series representations. This quantity describes the growth rate in the number of bits needed to specify the series coefficients in order to approximate the input-output map with increasing accuracy. Asymptotic estimates are then computed in terms of the growth rate of the series coefficients and the entropy of the generating series, which is an entirely distinct entropy concept. Once the results for the system identification entropy of a single system are established, the focus turns to interconnected systems, specifically, parallel, series, and feedback interconnected systems. Examples include estimating upper bounds for the system identification entropies of parallel interconnected rational systems and cascaded Wiener systems.