Identification of two-neuron FitzHugh-Nagumo model based on the speed-gradient and filtering

The paper is devoted to the parameter identification problem for two-neuron FitzHugh-Nagumo models under condition when only one variable, namely, the membrane potential, is measured. Another practical assumption is that both variable derivatives cannot be measured. Finally, it is assumed that the sensor measuring the membrane potential is imprecise, and all measurements have some unknown scaling factor. These circumstances bring additional difficulties to the parameters' estimation problem, and therefore, such case was not studied before. To solve the problem first, the model is transformed to a more simple form without unmeasurable variables. Variables obtained from applying a second-order real filter-differentiator are used instead of unmeasurable derivatives. Then, an adaptive system, parameters of which are estimates of original system parameters, is designed. The estimation (identification) goal is to properly adjust parameter estimates. To this end, the speed-gradient method is employed. The correctness of the obtained solution is proved theoretically and illustrated by computer simulation in the Simulink environment. The sufficient conditions of asymptotically correct identification for the speed-gradient method with integral objective function are formulated and proved. The novelty of the paper is that in contrast to existing solutions to the FitzHugh-Nagumo identification problem, we take into account a systematic error of the membrane potential measurement. Furthermore, the parameters are estimated for a system composed of two FitzHugh-Nagumo models, which open perspectives for using the proposed results for modeling and estimation of parameters for neuron population.