Abstract
This paper applies the classical prediction error method (PEM) to the estimation of nonlinear discrete-time models of neuronal systems subject to input-additive noise. While the nonlinear system exhibits excitability, bifurcations, and limit-cycle oscillations, we prove consistency of the parameter estimation procedure under output feedback. Hence, this paper provides a rigorous framework for the application of conventional nonlinear system identification methods to discrete-time stochastic neuronal systems. The main result exploits the elementary property that conductance-based models of neurons have an exponentially contracting inverse dynamics. This property is implied by the voltage-clamp experiment, which has been the fundamental modeling experiment of neurons ever since the pioneering work of Hodgkin and Huxley.
| Original language | English |
|---|---|
| Article number | 109297 |
| Number of pages | 13 |
| Journal | Automatica |
| Volume | 123 |
| DOIs | |
| Publication status | Published - Jan 2021 |
Funding
Thiago Burghi was supported by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) — Brasil (Finance Code 001 ). Maarten Schoukens was supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Fellowship (Grant Agreement No. 798627 ). The research leading to these results has received funding from the European Research Council under the Advanced ERC Grant Agreement Switchlet No. 670645 . The authors thank the anonymous reviewers, as well as Dr. Monika Josza, for helping to improve earlier versions of this manuscript.
| Funders | Funder number |
|---|---|
| European Union's Horizon 2020 - Research and Innovation Framework Programme | 670645, 798627 |
| H2020 European Research Council | |
| Coordenação de Aperfeiçoamento de Pessoal de Nível Superior |
Keywords
- Closed-loop identification
- Contraction analysis
- Neuronal models
- Nonlinear system identification
- Prediction error methods