2011/11/27 by Jr-Shin Li, Li, Jr-Shin, Isuru Dasanayake +3
Computer Science · Neuroscience · #Adaptation and Self-Organizing Systems (nlin.AO) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Neural dynamics and brain function #Nonlinear Dynamics and Pattern Formation #Optimization and Control (math.OC) #Photoreceptor and optogenetics research
paper · pdf · doi:10.48550/arxiv.1111.6306
openalex publication_date 2011/11/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.