Skip to main content

ORIGINAL RESEARCH article

Front. Comput. Neurosci.
Volume 18 - 2024 | doi: 10.3389/fncom.2024.1483100
This article is part of the Research Topic The mutual promotion of Control Science and Neuroscience View all articles

A framework for optimal control of oscillations and synchrony applied to nonlinear models of neural population dynamics

Provisionally accepted
Lena Salfenmoser Lena Salfenmoser 1*Klaus Obermayer Klaus Obermayer 1,2
  • 1 Technical University of Berlin, Berlin, Germany
  • 2 Bernstein Center for Computational Neuroscience Berlin, Berlin, Germany

The final, formatted version of the article will be published soon.

    We adapt nonlinear optimal control theory (OCT) to control oscillations and network synchrony and apply it to models of neural population dynamics. OCT is a mathematical framework to compute an efficient stimulation for dynamical systems. In its standard formulation, it requires a well-defined reference trajectory as target state. This requirement, however, may be overly restrictive for oscillatory targets, where the exact trajectory shape might not be relevant. To overcome this limitation, we introduce three alternative cost functionals to target oscillations and synchrony without specification of a reference trajectory. We successfully apply these cost functionals to single-node and network models of neural populations, in which each node is described by either the Wilson-Cowan model or a biophysically realistic high-dimensional meanfield model of exponential integrate-and-fire neurons. We compute efficient control strategies for four different control tasks. Firstly, we drive oscillations from a stable stationary state at a particular frequency. Secondly, we switch between stationary and oscillatory stable states and find a translational invariance of the state-switching control signals. Thirdly, we switch between in-phase and out-of-phase oscillations in a two-node network, where all cost functionals lead to identical OC signals in the minimum-energy limit. Finally, we (de-) synchronize an (a-) synchronously oscillating six-node network. In this setup, for the desynchronization task, we find very different control strategies for the three cost functionals. The suggested methods represent a toolbox that enables to include oscillatory phenomena into the framework of nonlinear OCT without specification of an exact reference trajectory. However, task-specific adjustments of the optimization parameters have to be performed in order to obtain informative results.

    Keywords: Nonlinear optimal control, Control of oscillations, control of synchrony, Control of neural dynamics, neural population models

    Received: 19 Aug 2024; Accepted: 18 Nov 2024.

    Copyright: © 2024 Salfenmoser and Obermayer. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

    * Correspondence: Lena Salfenmoser, Technical University of Berlin, Berlin, Germany

    Disclaimer: All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.