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An adaptive observer is designed for online estimation of Hilbert-Schmidtoperators from online measurement of the state for some class of nonlinearinfinite-dimensional dynamical systems. Convergence is ensured underdetectability and persistency of excitation assumptions. The class of systemsconsidered is motivated by an application to kernel reconstruction of neuralfields, commonly used to model spatiotemporal activity of neuronal populations.Numerical simulations confirm the relevance of the approach.

Online estimation of Hilbert-Schmidt operators and application to kernel reconstruction of neural fields