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

2025-08-27

AI Summary

Predictive feedback control for nonlinear systems with unknown and arbitrarily long actuator delays suffers from intractable analytical modeling. Method: This paper proposes a neural-operator-based predictive feedback control framework, introducing neural operators—trained to approximate infinite-dimensional delay dynamics—for the first time in controller design for delayed systems. Delay dynamics are modeled via transport-type partial differential equations, and semi-global practical convergence is rigorously established using Lyapunov–Krasovskii functional theory. The architecture employs offline training and online fast inference, ensuring both strong generalization and real-time capability. Contribution/Results: Evaluated on a biological activation/inhibition system, the method achieves a 15× speedup over conventional numerical prediction approaches, significantly enhancing control efficiency and practicality for highly delayed nonlinear systems.

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Abstract

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.

Problem

• Control nonlinear systems with unknown actuator delays
• Approximate predictor using neural operator mapping
• Provide stability analysis and validate with biological system

Innovation

• Neural operator mapping approximates predictor feedback
• Offline trained neural network enables fast online inference
• Lyapunov-Krasovskii functional ensures semi-global practical convergence