Optimization of external stimuli for populations of theta neurons via mean-field feedback control

TL;DR

This paper develops a mean-field control approach to design external stimuli that effectively synchronize theta neuron populations, with a focus on robustness and numerical solution methods.

Contribution

It introduces an optimal control framework for theta neurons using mean-field feedback, including a novel numerical descent method for solving the problem.

Findings

Successful numerical implementation of the control method.

Effective synchronization of neuron populations demonstrated.

Robustness of control against model variations shown.

Abstract

We study a problem of designing ``robust'' external excitations for control and synchronization of an assembly of homotypic harmonic oscillators representing so-called theta neurons. The model of theta neurons (Theta model) captures, in main, the bursting behavior of spiking cells in the brain of biological beings, enduring periodic oscillations of the electric potential in their membrane. We study the following optimization problem: to design an external stimulus (control), which steers all neurons of a given population to their desired phases (i.e., excites/slows down its spiking activity) with the highest probability. This task is formulated as an optimal mean-field control problem for the local continuity equation in the space of probability measures. To solve this problem numerically, we propose an indirect deterministic descent method based on an exact representation of the increment (infinite-order variation) of the objective functional. We discuss some aspects of practical realization of the proposed method, and provide results of numerical experiments.