# Stability-Preserving Online Adaptation of Neural Closed-loop Maps

arXiv: https://arxiv.org/abs/2603.22469 · HTML: https://mlsanity.com/paper/2603.22469/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 26 references that are in the map.
- First posted on arXiv 23 Mar 2026.

## Builds on (most cited first, 12 of 12)

- [Recurrent Equilibrium Networks: Flexible Dynamic Models with Guaranteed Stability and Robustness](https://mlsanity.com/paper/2104.05942/) (2021)
- [A Neural Network Approach Applied to Multi-Agent Optimal Control](https://mlsanity.com/paper/2011.04757/) (2020)
- [Neural System Level Synthesis: Learning over All Stabilizing Policies for Nonlinear Systems](https://mlsanity.com/paper/2203.11812/) (2022)
- [Youla-REN: Learning Nonlinear Feedback Policies with Robust Stability Guarantees](https://mlsanity.com/paper/2112.01253/) (2021)
- [Learning to Boost the Performance of Stable Nonlinear Systems](https://mlsanity.com/paper/2405.00871/) (2024)
- [Learning Over Contracting and Lipschitz Closed-Loops for Partially-Observed Nonlinear Systems (Extended Version)](https://mlsanity.com/paper/2304.06193/) (2023)
- [A System Level Approach to Discrete-Time Nonlinear Systems](https://mlsanity.com/paper/2004.08004/) (2020)
- [Structured state-space models are deep Wiener models](https://mlsanity.com/paper/2312.06211/) (2023)
- [Optimal distributed control with stability guarantees by training a network of neural closed-loop maps](https://mlsanity.com/paper/2404.02820/) (2024)
- [Parametrizations of All Stable Closed-loop Responses: From Theory to Neural Network Control Design](https://mlsanity.com/paper/2412.19280/) (2024)
- [Neural Port-Hamiltonian Models for Nonlinear Distributed Control: An Unconstrained Parametrization Approach](https://mlsanity.com/paper/2411.10096/) (2024)
- [Model Predictive Control for Multi-Agent Systems under Limited Communication and Time-Varying Network Topology](https://mlsanity.com/paper/2304.01649/) (2023)

## Abstract (arXiv)

The growing complexity of modern control tasks calls for controllers that can react online as objectives and disturbances change, while preserving closed-loop stability. Recent approaches for improving the performance of nonlinear systems while preserving closed-loop stability rely on time-invariant recurrent neural-network controllers, but offer no principled way to update the controller during operation. Most importantly, switching from one stabilizing policy to another can itself destabilize the closed-loop. We address this problem by introducing a stability-preserving update mechanism for nonlinear, neural-network-based controllers. Each controller is modeled as a causal operator with bounded ℓp-gain, and we derive gain-based conditions under which the controller may be updated online. These conditions yield two practical update schemes, time-scheduled and state-triggered, that guarantee the closed-loop remains ℓp-stable after any number of updates. Our analysis further shows that stability is decoupled from controller optimality, allowing approximate or early-stopped controller synthesis. We demonstrate the approach on nonlinear systems with time-varying objectives and disturbances, and show consistent performance improvements over static and naive online baselines while guaranteeing stability.