Distributed Identification of Contracting and/or Monotone Network Dynamics

TL;DR

This paper introduces scalable distributed methods for identifying large-scale network systems that guarantee stability and monotonicity, using convex constraints and ADMM, demonstrated on complex linear and nonlinear case studies.

Contribution

It develops a novel convex, separable model set enabling distributed identification with stability and monotonicity guarantees for large networks.

Findings

Successful application to a 200-dimensional nonlinear traffic network

Demonstrated scalability to networks with hundreds or thousands of nodes

Validated effectiveness on both linear and nonlinear case studies

Abstract

This paper proposes methods for identification of large-scale networked systems with guarantees that the resulting model will be contracting -- a strong form of nonlinear stability -- and/or monotone, i.e. order relations between states are preserved. The main challenges that we address are: simultaneously searching for model parameters and a certificate of stability, and scalability to networks with hundreds or thousands of nodes. We propose a model set that admits convex constraints for stability and monotonicity, and has a separable structure that allows distributed identification via the alternating directions method of multipliers (ADMM). The performance and scalability of the approach is illustrated on a variety of linear and non-linear case studies, including a nonlinear traffic network with a 200-dimensional state space.