Constrained minimum-power control of spiking neuron oscillators

In this article, we study optimal control problems of spiking neurons whose dynamics are described by a phase model. We design minimum-power current stimuli (controls) that lead to desired spiking times. In particular, we consider bounded control amplitude and characterize the range of possible spiking times according to the bound. The design of such bounded optimal controls is of fundamental importance as phase models are accurate under weak forcing. We show that for a given bound, the corresponding feasible spiking times are optimally achieved by switching controls. We present analytical expressions with numerical simulations of these minimum-power stimuli for various phase models of neurons.