Approximate optimal iterative approach for a class of oscillatory neuron models

Control of oscillatory neuron models becomes a growing interest due to the application of implanted stimulus electrodes in mitigating pathological behaviours. We present an approximate optimal iterative control method for minimum-current control of the FitzHugh-Nagumo model with external disturbance. We first focus on revealing optimality conditions based on the Pontryagin's maximum principle and constructing a related nonlinear two-point boundary value problem. Then, we transform the problem into two iterative sequences of linear differential equations. The control law is finally derived and composed of feedback and compensation terms which can be approximated using approximate iterative approach. Simulations illustrate the results.