Observing the state of networks with directed higher-order interactions

TL;DR

This paper introduces an algorithmic observer for reconstructing the states of nonlinear networks with directed higher-order interactions, validated through theoretical analysis and numerical experiments.

Contribution

It presents a novel observer design method that selects measured nodes and gains for nonlinear networks with complex interactions, supported by convergence proofs.

Findings

The observer guarantees convergence under certain conditions.

Numerical experiments demonstrate robustness and effectiveness.

Application to opinion dynamics shows practical utility.

Abstract

We consider the problem of reconstructing the state of a network of nonlinear dynamical systems in the presence of directed higher-order interactions. Grounded on analytical convergence results, we propose an algorithmic observer design procedure that simultaneously selects the nodes to be measured and the observer gains. We complement the theoretical analysis with an exhaustive numerical investigation campaign that showcases the performance and robustness of the designed observer. Finally, the algorithmic procedure is used to fully reconstruct the opinions of a group of agents.