# Delay-adaptive Control of Nonlinear Systems with Approximate Neural Operator Predictors

arXiv: https://arxiv.org/abs/2508.20367 · HTML: https://mlsanity.com/paper/2508.20367/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 44 references that are in the map.
- First posted on arXiv 28 Aug 2025.

## Builds on (most cited first, 17 of 17)

- [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)
- [Nonlocality and Nonlinearity Implies Universality in Operator Learning](https://mlsanity.com/paper/2304.13221/) (2023)
- [Neural Operators for Bypassing Gain and Control Computations in PDE Backstepping](https://mlsanity.com/paper/2302.14265/) (2023)
- [Data Complexity Estimates for Operator Learning](https://mlsanity.com/paper/2405.15992/) (2024)
- [Discretization Error of Fourier Neural Operators](https://mlsanity.com/paper/2405.02221/) (2024)
- [Neural Operators of Backstepping Controller and Observer Gain Functions for Reaction-Diffusion PDEs](https://mlsanity.com/paper/2303.10506/) (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)
- [Neural Operators for Predictor Feedback Control of Nonlinear Delay Systems](https://mlsanity.com/paper/2411.18964/) (2024)
- [Deep Learning of Delay-Compensated Backstepping for Reaction-Diffusion PDEs](https://mlsanity.com/paper/2308.10501/) (2023)
- [Adaptive Neural-Operator Backstepping Control of a Benchmark Hyperbolic PDE](https://mlsanity.com/paper/2401.07862/) (2024)
- [Neural Operators for Boundary Stabilization of Stop-and-go Traffic](https://mlsanity.com/paper/2312.10374/) (2023)
- [Size Lowerbounds for Deep Operator Networks](https://mlsanity.com/paper/2308.06338/) (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)
- [Safety-Critical Control with Input Delay in Dynamic Environment](https://mlsanity.com/paper/2112.08445/) (2021)

## Built on by (most cited first, 1 of 1)

- [Delay compensation of multi-input distinct delay nonlinear systems via neural operators](https://mlsanity.com/paper/2509.17131/) (2025)

## Abstract (arXiv)

In this work, we propose a rigorous method for implementing predictor feedback controllers in nonlinear systems with unknown and arbitrarily long actuator delays. To address the analytically intractable nature of the predictor, we approximate it using a learned neural operator mapping. This mapping is trained once, offline, and then deployed online, leveraging the fast inference capabilities of neural networks. We provide a theoretical stability analysis based on the universal approximation theorem of neural operators and the transport partial differential equation (PDE) representation of the delay. We then prove, via a Lyapunov-Krasovskii functional, semi-global practical convergence of the dynamical system dependent on the approximation error of the predictor and delay bounds. Finally, we validate our theoretical results using a biological activator/repressor system, demonstrating speedups of 15 times compared to traditional numerical methods.