# Distributed Identification of Contracting and/or Monotone Network Dynamics

arXiv: https://arxiv.org/abs/2107.14309 · HTML: https://mlsanity.com/paper/2107.14309/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 71 references that are in the map.
- First posted on arXiv 29 Jul 2021.

## Builds on (most cited first, 18 of 18)

- [Stable Recurrent Models](https://mlsanity.com/paper/1805.10369/) (2018)
- [A flexible state space model for learning nonlinear dynamical systems](https://mlsanity.com/paper/1603.05486/) (2016)
- [On the smoothness of nonlinear system identification](https://mlsanity.com/paper/1905.00820/) (2019)
- [Contracting Implicit Recurrent Neural Networks: Stable Models with Improved Trainability](https://mlsanity.com/paper/1912.10402/) (2019)
- [Convergence Properties for Discrete-time Nonlinear Systems](https://mlsanity.com/paper/1612.05327/) (2016)
- [Convex Parameterizations and Fidelity Bounds for Nonlinear Identification and Reduced-Order Modelling](https://mlsanity.com/paper/1701.06652/) (2017)
- [Specialized Interior Point Algorithm for Stable Nonlinear System Identification](https://mlsanity.com/paper/1803.01066/) (2018)
- [Subspace identification of large-scale interconnected systems](https://mlsanity.com/paper/1309.5105/) (2013)
- [Identifiability of linear dynamic networks](https://mlsanity.com/paper/1609.00864/) (2016)
- [Separable and Localized System Level Synthesis for Large-Scale Systems](https://mlsanity.com/paper/1701.05880/) (2017)
- [On Existence of Separable Contraction Metrics for Monotone Nonlinear Systems](https://mlsanity.com/paper/1704.02676/) (2017)
- [Throughput Optimality and Overload Behavior of Dynamical Flow Networks under Monotone Distributed Routing](https://mlsanity.com/paper/1308.1993/) (2013)
- [Convexity and Robustness of Dynamic Traffic Assignment and Freeway Network Control](https://mlsanity.com/paper/1509.06189/) (2015)
- [Formal Synthesis of Control Strategies for Positive Monotone Systems](https://mlsanity.com/paper/1702.08501/) (2017)
- [A Contractive Approach to Separable Lyapunov Functions for Monotone Systems](https://mlsanity.com/paper/1704.04218/) (2017)
- [Identification in Dynamic Networks](https://mlsanity.com/paper/1710.08865/) (2017)
- [Distributed Nonlinear Control Design using Separable Control Contraction Metrics](https://mlsanity.com/paper/1810.04794/) (2018)
- [Priority Maps for Surveillance and Intervention of Wildfires and other Spreading Processes](https://mlsanity.com/paper/1903.11204/) (2019)

## Abstract (arXiv)

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.