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Synchronization of oscillations is a phenomenon prevalent in natural, social, and engineering systems. Controlling synchronization of oscillating systems is motivated by a wide range of applications from surgical treatment of neurological diseases to the design of neurocomputers. In this paper, we study the control of an ensemble of uncoupled neuron oscillators described by phase models. We examine...
In this paper, we investigate the fundamental limits on how the inter-spike time of a neuron oscillator can be perturbed by the application of an external control input (a current stimulus) with zero net electric charge accumulation. We derive the minimum and maximum inter-spike time assignment controls for phase models using the maximum principle, and fully characterize the possible range of neuronal...
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...
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