Persistence of Excitation in Uniformly Embedded Reproducing Kernel Hilbert (RKH) Spaces

19 Feb 2020 Guo Jia Paruchuri Sai Tej Kurdila Andrew J.

This paper introduces two new notions of the persistence of excitation (PE) in reproducing kernel Hilbert (RKH) spaces that can be used to establish the convergence of function estimates generated by the RKH space embedding method. The equivalence of these two PE conditions is shown to hold if $\mathbb{U}(\bar{S}_1)$ is uniformly equicontinuous, where $\mathbb{U}$ is the Koopman operator and $\bar{S}_1$ is the closed unit sphere in the RKH space... (read more)

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