Adaptive Observers for Biophysical Neuronal Circuits

This article presents adaptive observers for online state and parameter estimation of a class of nonlinear systems motivated by biophysical models of neuronal circuits. We first present a linear-in-the-parameters design that solves a classical RLS problem. Then, building on this simple design, we present an augmented adaptive observer for models with a nonlinearly parameterized internal dynamics, the parameters of which we interpret as structured uncertainty. We present a convergence and robustness analysis based on contraction theory, and illustrate the potential of the approach in neurophysiological applications by means of numerical simulations.