Non-negative inputs for underactuated control of spiking in coupled integrate-and-fire neurons

A rapidly growing area of research in neuroscience pertains to the use of external stimulation to manipulate the activity in ensembles of neurons. When such activity is modeled as the output of a dynamical system, the overall neurostimulation problem can be framed in the context of systems and control. Here, we present a particular form of control design for neurostimulation: the manipulation of spike timing with underactuated inputs. We first discuss formulations for spike sequence and pattern controllability, which relax the classical notions of controllability. Then, motivated by particular neurostimulation technologies, we discuss control design for achieving spike sequences and patterns with piecewise constant non-negative inputs in a model consisting of coupled integrate-and-fire neurons. The results provide the basis for a range of control theoretic studies related to manipulation of spiking dynamics in biophysical neuronal networks.