Stabilization of nonlinear systems with unknown delays via delay-adaptive neural operator approximate predictors
Not on the map. Why?
Abstract (arXiv)
This work establishes the first rigorous stability guarantees for approximate predictors in delay-adaptive control of nonlinear systems, addressing a key challenge in practical implementations where exact predictors are unavailable. We analyze two scenarios: (i) when the actuated input is directly measurable, and (ii) when it is estimated online. For the measurable input case, we prove semi-global practical asymptotic stability with an explicit bound proportional to the approximation error ε. For the unmeasured input case, we demonstrate local practical asymptotic stability, with the region of attraction explicitly dependent on both the initial delay estimate and the predictor approximation error. To bridge theory and practice, we show that neural operators-a flexible class of neural network-based approximators-can achieve arbitrarily small approximation errors, thus satisfying the conditions of our stability theorems. Numerical experiments on two nonlinear benchmark systems-a biological protein activator/repressor model and a micro-organism growth Chemostat model-validate our theoretical results. In particular, our numerical simulations confirm stability under approximate predictors, highlight the strong generalization capabilities of neural operators, and demonstrate a substantial computational speedup of up to 15x compared to a baseline fixed-point method.
Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 18 of its 51 references that are in the map. First posted on arXiv 30 Sep 2025.
Builds on
18 of 51 references.
References · 18
- 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
- 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 2,018
- 2023Nonlocality and Nonlinearity Implies Universality in Operator Learningcited by 43
- 2023Neural Operators for Bypassing Gain and Control Computations in PDE Backsteppingcited by 29
- 2024Data Complexity Estimates for Operator Learningcited by 26
- 2024Discretization Error of Fourier Neural Operatorscited by 22
- 2023Neural Operators of Backstepping Controller and Observer Gain Functions for Reaction-Diffusion PDEscited by 18
- 2023Neural Operators for PDE Backstepping Control of First-Order Hyperbolic PIDE with Recycle and Delaycited by 13
- 2024Gain Scheduling with a Neural Operator for a Transport PDE with Nonlinear Recirculationcited by 9
- 2024Neural Operators for Predictor Feedback Control of Nonlinear Delay Systemscited by 9
- 2023Deep Learning of Delay-Compensated Backstepping for Reaction-Diffusion PDEscited by 8
- 2024Adaptive Neural-Operator Backstepping Control of a Benchmark Hyperbolic PDEcited by 8
6 more
- 2023Neural Operators for Boundary Stabilization of Stop-and-go Trafficcited by 7
- 2023Size Lowerbounds for Deep Operator Networkscited by 6
- 2024Adaptive control of reaction-diffusion PDEs via neural operator-approximated gain kernelscited by 5
- 2015Predictor-Feedback Stabilization of Multi-Input Nonlinear Systemscited by 4
- 2021Safety-Critical Control with Input Delay in Dynamic Environmentcited by 3
- 2025Global Stabilization of Chemostats with Nonzero Mortality and Substrate Dynamicscited by 1
Built on by
Citing papers per year: 2026: 2.
2 papers.