# Neural Operators for Predictor Feedback Control of Nonlinear Delay Systems

arXiv: https://arxiv.org/abs/2411.18964 · HTML: https://mlsanity.com/paper/2411.18964/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 55 references that are in the map.
- First posted on arXiv 28 Nov 2024.

## Builds on (most cited first, 21 of 21)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [GNOT: A General Neural Operator Transformer for Operator Learning](https://mlsanity.com/paper/2302.14376/) (2023)
- [Neural Operators for Accelerating Scientific Simulations and Design](https://mlsanity.com/paper/2309.15325/) (2023)
- [NOMAD: Nonlinear Manifold Decoders for Operator Learning](https://mlsanity.com/paper/2206.03551/) (2022)
- [Neural Operator Learning for Long-Time Integration in Dynamical Systems with Recurrent Neural Networks](https://mlsanity.com/paper/2303.02243/) (2023)
- [Neural Operators for Bypassing Gain and Control Computations in PDE Backstepping](https://mlsanity.com/paper/2302.14265/) (2023)
- [Learning Stochastic Dynamical System via Flow Map Operator](https://mlsanity.com/paper/2305.03874/) (2023)
- [Neural Operators for PDE Backstepping Control of First-Order Hyperbolic PIDE with Recycle and Delay](https://mlsanity.com/paper/2307.11436/) (2023)
- [Gain Scheduling with a Neural Operator for a Transport PDE with Nonlinear Recirculation](https://mlsanity.com/paper/2401.02511/) (2024)
- [Adaptive Neural-Operator Backstepping Control of a Benchmark Hyperbolic PDE](https://mlsanity.com/paper/2401.07862/) (2024)
- [Machine Learning Accelerated PDE Backstepping Observers](https://mlsanity.com/paper/2211.15044/) (2022)
- [Neural Operators for Boundary Stabilization of Stop-and-go Traffic](https://mlsanity.com/paper/2312.10374/) (2023)
- [Adaptive control of reaction-diffusion PDEs via neural operator-approximated gain kernels](https://mlsanity.com/paper/2407.01745/) (2024)
- [Predictor-Feedback Stabilization of Multi-Input Nonlinear Systems](https://mlsanity.com/paper/1508.05756/) (2015)
- [Distributed Optimal Voltage Control with Asynchronous and Delayed Communication](https://mlsanity.com/paper/1903.01065/) (2019)
- [Stability Results for the Continuity Equation](https://mlsanity.com/paper/1908.05995/) (2019)
- [Learning flow functions of spiking systems](https://mlsanity.com/paper/2312.11913/) (2023)
- [Input-to-State Stability in sup norms for hyperbolic systems with boundary disturbances](https://mlsanity.com/paper/2004.12026/) (2020)

## Built on by (most cited first, 9 of 9)

- [Deep Operator Neural Network Model Predictive Control](https://mlsanity.com/paper/2505.18008/) (2025)
- [Delay compensation of multi-input distinct delay nonlinear systems via neural operators](https://mlsanity.com/paper/2509.17131/) (2025)
- [Stabilization of nonlinear systems with unknown delays via delay-adaptive neural operator approximate predictors](https://mlsanity.com/paper/2509.26443/) (2025)
- [Topological DeepONets and a generalization of the Chen-Chen operator approximation theorem](https://mlsanity.com/paper/2603.11972/) (2026)
- [Delay-adaptive Control of Nonlinear Systems with Approximate Neural Operator Predictors](https://mlsanity.com/paper/2508.20367/) (2025)
- [Predictor-Based Output-Feedback Control of Linear Systems with Time-Varying Input and Measurement Delays via Neural-Approximated Prediction Horizons](https://mlsanity.com/paper/2603.29117/) (2026)
- [Sampling-Horizon Neural Operator Predictors for Nonlinear Control under Delayed Inputs](https://mlsanity.com/paper/2603.29119/) (2026)
- [Neural Operators for Design-Space Surrogate Modeling of Tendon-Actuated Continuum Robots](https://mlsanity.com/paper/2605.19104/) (2026)
- [Families of Control-Cost-Parametrized Inverse-Optimal Universal Stabilizers](https://mlsanity.com/paper/2606.09047/) (2026)

## Abstract (arXiv)

Predictor feedback designs are critical for delay-compensating controllers in nonlinear systems. However, these designs are limited in practical applications as predictors cannot be directly implemented, but require numerical approximation schemes, which become computationally prohibitive when system dynamics are expensive to compute. To address this challenge, we recast the predictor design as an operator learning problem, and learn the predictor mapping via a neural operator. We prove the existence of an arbitrarily accurate neural operator approximation of the predictor operator. Under the approximated predictor, we achieve semiglobal practical stability of the closed-loop nonlinear delay system. The estimate is semiglobal in a unique sense - one can enlarge the set of initial states as desired, though this increases the difficulty of training a neural operator, which appears practically in the stability estimate. Furthermore, our analysis holds for any black-box predictor satisfying the universal approximation error bound. We demonstrate the approach by controlling a 5-link robotic manipulator with different neural operator models, achieving significant speedups compared to classic predictor feedback schemes while maintaining closed-loop stability.