Online estimation of biophysical neural networks

Abstract

This paper presents an adaptive observer for online state and parameter estimation of a broad class of biophysical models of neuronal networks. The design closely resembles classical solutions of adaptive control, and the convergence proof is based on contraction analysis. Our results include robustness guarantees with respect to unknown parameter dynamics. We discuss the potential of the approach in neurophysiological applications.

Adaptive Conductance Control

“…A detailed introduction to such models can be found in [13,14]. In this section, we extend the system-theoretic conductance-based modelling framework found in [11].…”

“…and I int ∈ R nv , I ext ∈ R nv and u ∈ R nv are formed by gathering the intrinsic and extrinsic currents and inputs of each neuron in the corresponding n v -dimensional vectors. The addition of gap junction currents extends the system-theoretic modelling framework of [11].…”

“…The recent work [11] provides an adaptive observer to estimate the parameters of the system (7) in real-time. This observer has global convergence properties and is based on the recursive least squares algorithm.…”

“…We show that these properties can be exploited in conductance-based electrical circuits in the same way as they have been exploited in the impedancebased mechanical circuits of robotics. A core element of the proposed adaptive control design is the adaptive observer recently proposed for real-time estimation of conductance-based models in [11].…”

“…Section 2 introduces conductance-based models, including the specific parametrisation we will require. Section 3 summarises the adaptive observer design detailed in [11]. Section 4 employs this observer to solve the basic problems of adaptive reference tracking and adaptive disturbance rejection, as well as showing the relevance of such problems in the control of a simple biophysical neural network.…”