# Youla-REN: Learning Nonlinear Feedback Policies with Robust Stability Guarantees

arXiv: https://arxiv.org/abs/2112.01253 · HTML: https://mlsanity.com/paper/2112.01253/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 27 references that are in the map.
- First posted on arXiv 2 Dec 2021.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Concrete Problems in AI Safety](https://mlsanity.com/paper/1606.06565/) (2016)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learning](https://mlsanity.com/paper/2108.06266/) (2021)
- [Safe Model-based Reinforcement Learning with Stability Guarantees](https://mlsanity.com/paper/1705.08551/) (2017)
- [Neural Lyapunov Control](https://mlsanity.com/paper/2005.00611/) (2020)
- [Implicit Deep Learning](https://mlsanity.com/paper/1908.06315/) (2019)
- [Learning for Safety-Critical Control with Control Barrier Functions](https://mlsanity.com/paper/1912.10099/) (2019)
- [Lyapunov-stable neural-network control](https://mlsanity.com/paper/2109.14152/) (2021)
- [Recurrent Equilibrium Networks: Flexible Dynamic Models with Guaranteed Stability and Robustness](https://mlsanity.com/paper/2104.05942/) (2021)
- [Control Contraction Metrics: Convex and Intrinsic Criteria for Nonlinear Feedback Design](https://mlsanity.com/paper/1503.03144/) (2015)
- [Recurrent Neural Network Controllers Synthesis with Stability Guarantees for Partially Observed Systems](https://mlsanity.com/paper/2109.03861/) (2021)
- [Reduced-Order Nonlinear Observers via Contraction Analysis and Convex Optimization](https://mlsanity.com/paper/2012.06158/) (2020)
- [Nonlinear parameter-varying state-feedback design for a gyroscope using virtual control contraction metrics](https://mlsanity.com/paper/2104.04917/) (2021)

## Built on by (most cited first, 10 of 10)

- [Direct Parameterization of Lipschitz-Bounded Deep Networks](https://mlsanity.com/paper/2301.11526/) (2023)
- [Learning over All Stabilizing Nonlinear Controllers for a Partially-Observed Linear System](https://mlsanity.com/paper/2112.04219/) (2021)
- [Synthesis of Stabilizing Recurrent Equilibrium Network Controllers](https://mlsanity.com/paper/2204.00122/) (2022)
- [Unconstrained Parametrization of Dissipative and Contracting Neural Ordinary Differential Equations](https://mlsanity.com/paper/2304.02976/) (2023)
- [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)
- [Optimisation of Structured Neural Controller Based on Continuous-Time Policy Gradient](https://mlsanity.com/paper/2201.06262/) (2022)
- [RobustNeuralNetworks.jl: a Package for Machine Learning and Data-Driven Control with Certified Robustness](https://mlsanity.com/paper/2306.12612/) (2023)
- [React to Surprises: Stable-by-Design Neural Feedback Control and the Youla-REN](https://mlsanity.com/paper/2506.01226/) (2025)
- [Stability-Preserving Online Adaptation of Neural Closed-loop Maps](https://mlsanity.com/paper/2603.22469/) (2026)

## Abstract (arXiv)

This paper presents a parameterization of nonlinear controllers for uncertain systems building on a recently developed neural network architecture, called the recurrent equilibrium network (REN), and a nonlinear version of the Youla parameterization. The proposed framework has "built-in" guarantees of stability, i.e., all policies in the search space result in a contracting (globally exponentially stable) closed-loop system. Thus, it requires very mild assumptions on the choice of cost function and the stability property can be generalized to unseen data. Another useful feature of this approach is that policies are parameterized directly without any constraints, which simplifies learning by a broad range of policy-learning methods based on unconstrained optimization (e.g. stochastic gradient descent). We illustrate the proposed approach with a variety of simulation examples.