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The operation of the nervous system, consequently the various dynamic neuron models, show strong nonlinearities. Their control, that may result in the treatment of various diseases, have to cope with the essential difficulties as the great deviations/uncertainties in the parameters of the available models, and the time-delay related to the observations of the measurable quantities, the computation, and the exertion of the control signal. For tackling model uncertainties a novel, fixed point transformation (FPT)-based adaptive control approach was suggested that generally works by the use of fresh observations on the behavior of the controlled system, therefore its operation may be degraded by time-delay effects. Furthermore, in the practice time-delay effects can be reduced by using model-based extrapolation of the motion of the controlled system for the “dead period” spanned between the observation and the actual appearance of the control action. In the lack of reliable dynamic model such an extrapolation may be questionable. In this research, up to or knowledge, at first time, time-delay effects are studied in the FPT-based adaptive control of the FitzHugh-Nagumo Neuron Model using novel fractional order kinematic feedback terms. This neuron is a relevant paradigm because showing very sharp nonlinearities in its dynamics. It is concluded that the use of an approximation-based extrapolation in a control of this special fractional order PID-type feedback can considerably reduce the consequences of the time-delay problems.

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Fractional Order PID-type Feedback in Fixed Point Transformation-based Adaptive Control of the FitzHugh-Nagumo Neuron Model with Time-delay ⁎ ⁎This project has received funding from the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation programme (grant agreement No 679681). Tamás Faitli has been supported by the “New National Excellence Program of the Ministry of Human Capacities”, application number UNKP-17-1-I, for the period 01 September 2017 – 30 June 2018.