Minimum effort decentralized control design for contracting network systems

TL;DR

This paper presents a method for designing minimal effort local controllers to ensure contraction in networked systems, using hierarchical contraction characterization and matrix-balancing techniques, demonstrated on neural networks.

Contribution

It introduces a novel approach combining hierarchical contraction and matrix-balancing to achieve decentralized control with minimal effort.

Findings

Successfully stabilizes a network of FitzHugh-Nagumo neurons

Provides a systematic way to design local controllers for contraction

Applicable to networks with general interaction topologies

Abstract

We consider the problem of making a networked system contracting by designing minimal effort local controllers. Our method combines a hierarchical contraction characterization and a matrix-balancing approach to stabilizing a Metzler matrix via minimal diagonal perturbations. We demonstrate our approach by designing local controllers that render contractive a network of FitzHugh-Nagumo neurons with a general topology of interactions.