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 neurological treatment of
Parkinson's disease to the design of neurocomputers. In this article, we study
the control of an ensemble of uncoupled neuron oscillators described by phase
models. We examine controllability of such a neuron ensemble for various phase
models and, furthermore, study the related optimal control problems. In
particular, by employing Pontryagin's maximum principle, we analytically derive
optimal controls for spiking single- and two-neuron systems, and analyze the
applicability of the latter to an ensemble system. Finally, we present a robust
computational method for optimal control of spiking neurons based on
pseudospectral approximations. The methodology developed here is universal to
the control of general nonlinear phase oscillators.Comment: 29 pages, 6 figure