Flatness of Networks of Synaptically Coupled Excitatory-Inhibitory Neural Modules

¹ Quartz EA7393 Laboratory, ENSEA, 6 Avenue du Ponceau, 95014 Cergy-Pontoise, France
² Université Paris-Saclay, CNRS, CentraleSupélec, Laboratoire des signaux et systèmes, 3 Rue Joliot-Curie, 91192 Gif-sur-Yvette Cedex, France

^* Corresponding author: florentina.nicolau@ensea.fr

Received: 23 May 2022
Accepted: 12 November 2023

Abstract

In this paper, we consider networks of N synaptically coupled excitatory-inhibitory neural modules, with N arbitrary. It has been argued that the connection strengths may slowly vary with respect to time and that they can actually be considered as inputs of the network. The problem that we are studying is which connection strengths should be modified (in other words, which connection strengths should be considered as inputs) in order to achieve flatness for the resulting control system. Flatness of the control network depends on the number of inputs and we show that if enough connection strengths (at least N) can be considered as inputs, then the control network is flat without structural conditions. If the number of inputs is smaller than N. then flatness imposes particular configurations of the interactions between the subnetworks. Our main contribution is to identify, analyze and characterize several flat configurations in the latter case.