Data-Driven Global Stabilization of Unknown Infinite Networks

TL;DR

This paper presents a novel data-driven method for stabilizing unknown infinite networks by constructing ISS Lyapunov functions for subsystems and combining them via a small-gain framework to ensure global stability.

Contribution

It introduces a scalable, data-driven approach to stabilize infinite networks with unknown nonlinear subsystems using a compositional Lyapunov function framework.

Findings

Successfully stabilizes infinite networks of spacecraft, Lorenz systems, and a state-dependent control system.

Constructs ISS Lyapunov functions from noise-corrupted data for each subsystem.

Demonstrates global UGAS of the entire network through a small-gain compositional approach.

Abstract

This paper develops a direct data-driven framework for infinite networks with unknown nonlinear polynomial subsystems, enabling the synthesis of controllers that ensure the entire network is uniformly globally asymptotically stable (UGAS). To address scalability challenges arising from high dimensionality, we develop a data-driven approach to construct an input-to-state stable (ISS) Lyapunov function and its corresponding controller for each unknown subsystem using only a single set of noise-corrupted input-state trajectories collected from that subsystem. Once each subsystem admits a data-driven ISS Lyapunov function, we leverage a compositional small-gain framework for infinite-dimensional spaces to construct a global control Lyapunov function and its associated controller, thereby ensuring UGAS of the entire infinite network. The effectiveness of the proposed data-driven approach is demonstrated through three case studies, including infinite networks of spacecraft, Lorenz chaotic systems, and an academic example with a state-dependent control input matrix.