Adaptive observers for biophysical neuronal circuits

TL;DR

This paper introduces adaptive observers for real-time estimation of states and parameters in nonlinear biophysical neuronal models, combining linear and nonlinear parameterization techniques with robustness analysis.

Contribution

It develops a novel augmented adaptive observer framework for nonlinear neuronal models, with convergence guarantees and robustness analysis based on contraction theory.

Findings

Effective online estimation demonstrated through numerical simulations

Robustness of the observer shown via contraction theory analysis

Applicable to biophysical models of neuronal circuits

Abstract

This paper 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 recursive least squares 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.