LILAD: Learning In-context Lyapunov-stable Adaptive Dynamics Models

TL;DR

LILAD is a novel framework that combines in-context learning with Lyapunov stability theory to create adaptive, stable dynamics models capable of rapid generalization to new systems using minimal data.

Contribution

LILAD introduces a unified approach for system identification that ensures both stability and adaptability through joint learning of dynamics and Lyapunov functions via in-context learning.

Findings

Outperforms baseline models in predictive accuracy on benchmark systems.

Guarantees stability even under distribution shifts and out-of-task scenarios.

Enables rapid adaptation to new systems with minimal trajectory data.

Abstract

System identification in control theory aims to approximate dynamical systems from trajectory data. While neural networks have demonstrated strong predictive accuracy, they often fail to preserve critical physical properties such as stability and typically assume stationary dynamics, limiting their applicability under distribution shifts. Existing approaches generally address either stability or adaptability in isolation, lacking a unified framework that ensures both. We propose LILAD (Learning In-Context Lyapunov-stable Adaptive Dynamics), a novel framework for system identification that jointly guarantees adaptability and stability. LILAD simultaneously learns a dynamics model and a Lyapunov function through in-context learning (ICL), explicitly accounting for parametric uncertainty. Trained across a diverse set of tasks, LILAD produces a stability-aware, adaptive dynamics model alongside an adaptive Lyapunov certificate. At test time, both components adapt to a new system instance using a short trajectory prompt, which enables fast generalization. To rigorously ensure stability, LILAD also computes a state-dependent attenuator that enforces a sufficient decrease condition on the Lyapunov function for any state in the new system instance. This mechanism extends stability guarantees even under out-of-distribution and out-of-task scenarios. We evaluate LILAD on benchmark autonomous systems and demonstrate that it outperforms adaptive, robust, and non-adaptive baselines in predictive accuracy.