Time optimal control of spiking neurons.

By injecting an electrical current control stimulus into a neuron, one can change its inter-spike intervals. In this paper, we investigate the time optimal control problem for periodically firing neurons, represented by different one-dimensional phase models, and find analytical expressions for the minimum and maximum values of inter-spike intervals achievable with small bounded control stimuli. We consider two cases: with a charge-balance constraint on the input, and without it. The analytical calculations are supported with numerical results for examples of qualitatively different neuron models.