Iterative learning control algorithm for spiking behavior of neuron model

Controlling neurons to generate a desired or normal spiking behavior is the fundamental building block of the treatment of many neurologic diseases. The objective of this work is to develop a novel control method-closed-loop proportional integral (PI)-type iterative learning control (ILC) algorithm to control the spiking behavior in model neurons. In order to verify the feasibility and effectiveness of the proposed method, two single-compartment standard models of different neuronal excitability are specifically considered: Hodgkin-Huxley (HH) model for class 1 neural excitability and Morris-Lecar (ML) model for class 2 neural excitability. ILC has remarkable advantages for the repetitive processes in nature. To further highlight the superiority of the proposed method, the performances of the iterative learning controller are compared to those of classical PI controller. Either in the classical PI control or in the PI control combined with ILC, appropriate background noises are added in neuron models to approach the problem under more realistic biophysical conditions. Simulation results show that the controller performances are more favorable when ILC is considered, no matter which neuronal excitability the neuron belongs to and no matter what kind of firing pattern the desired trajectory belongs to. The error between real and desired output is much smaller under ILC control signal, which suggests ILC of neuron's spiking behavior is more accurate.