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We use conductance based neuron models and the mathematical modeling ofOptogenetics to define controlled neuron models and we address the minimal timecontrol of these affine systems for the first spike from equilibrium. We applytools of geometric optimal control theory to study singular extremals and weimplement a direct method to compute optimal controls. When the system is toolarge to theoretically investigate the existence of singular optimal controls,we observe numerically the optimal bang-bang controls.

Minimal time spiking in various ChR2-controlled neuron models