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

• URL: http://arxiv.org/abs/2508.20367v1
• Date: Thu, 28 Aug 2025 02:30:53 GMT
• Title: Delay-adaptive Control of Nonlinear Systems with Approximate Neural Operator Predictors
• Authors: Luke Bhan, Miroslav Krstic, Yuanyuan Shi,
• Abstract summary: We propose a rigorous method for implementing predictor feedback controllers in nonlinear systems with unknown and arbitrarily long actuator delays.<n>To address the analytically intractable nature of the predictor, we approximate it using a learned neural operator mapping.<n>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.<n>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.
• Score: 6.093618731228799
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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