This paper describes the solution of previously unconsidered identification problem for a network of arbitrary number of FitzHugh–Nagumo neuron models under disturbances. This problem is addressed under highly realistic yet challenging assumptions: the algorithm uses only the values of the neuron electric potential, while all other variables and their derivatives of the model are considered unmeasurable. Additionally, it is assumed that each equation in the system is subject to an unknown but bounded perturbation. The solution involves transforming the model into a simpler form using differentiating filters, followed by the application of one of two robustified versions of the speed-gradient algorithm. The first approach to robustification introduces a dead zone, preventing the algorithm from parameters over-tuning under the influence of disturbances. The second approach incorporates negative feedback into the parameter adjustment law. For both variants, theorems providing sufficient conditions for correct identification are formulated and proven in the general case. The obtained results are then applied to the network of FitzHugh–Nagumo models. Computer simulations of the designed systems illustrate the advantages of the approximated algorithms over the classical one in the presence of disturbances. The proposed approach can be applied to human brain modeling. For example, extremely noisy EEG signals could be used as the measured variables of the network connecting mathematical neural models with empirical data collected by neurophysiologists.
Rybalko et al. (Thu,) studied this question.