# Delay compensation of multi-input distinct delay nonlinear systems via neural operators

arXiv: https://arxiv.org/abs/2509.17131 · HTML: https://mlsanity.com/paper/2509.17131/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 34 references that are in the map.
- First posted on arXiv 21 Sep 2025.

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

- [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)
- [Neural Operator: Learning Maps Between Function Spaces](https://mlsanity.com/paper/2108.08481/) (2021)
- [Real-time high-resolution CO2 geological storage prediction using nested Fourier neural operators](https://mlsanity.com/paper/2210.17051/) (2022)
- [Neural Operators for Bypassing Gain and Control Computations in PDE Backstepping](https://mlsanity.com/paper/2302.14265/) (2023)
- [Neural Operators of Backstepping Controller and Observer Gain Functions for Reaction-Diffusion PDEs](https://mlsanity.com/paper/2303.10506/) (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)
- [Predictor-Feedback Stabilization of Multi-Input Nonlinear Systems](https://mlsanity.com/paper/1508.05756/) (2015)
- [Linear Supervision for Nonlinear, High-Dimensional Neural Control and Differential Games](https://mlsanity.com/paper/2412.02033/) (2024)
- [Networked control systems in the presence of scheduling protocols and communication delays](https://mlsanity.com/paper/1408.0147/) (2014)
- [Event-Triggered Stabilization of Nonlinear Systems with Time-Varying Sensing and Actuation Delay](https://mlsanity.com/paper/1709.02055/) (2017)
- [Experimental Implementation and Validation of Predictor-Based CACC for Vehicular Platoons With Distinct Actuation Delays](https://mlsanity.com/paper/2507.21579/) (2025)
- [Delay-adaptive Control of Nonlinear Systems with Approximate Neural Operator Predictors](https://mlsanity.com/paper/2508.20367/) (2025)

## Built on by (most cited first, 2 of 2)

- [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)

## Abstract (arXiv)

In this work, we present the first stability results for approximate predictors in multi-input non-linear systems with distinct actuation delays. We show that if the predictor approximation satisfies a uniform (in time) error bound, semi-global practical stability is correspondingly achieved. For such approximators, the required uniform error bound depends on the desired region of attraction and the number of control inputs in the system. The result is achieved through transforming the delay into a transport PDE and conducting analysis on the coupled ODE-PDE cascade. To highlight the viability of such error bounds, we demonstrate our results on a class of approximators - neural operators - showcasing sufficiency for satisfying such a universal bound both theoretically and in simulation on a mobile robot experiment.