Delay-adaptive Control of Nonlinear Systems with Approximate Neural Operator Predictors
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914010846199808 |
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| author | Bhan, Luke Krstic, Miroslav Shi, Yuanyuan |
| author_facet | Bhan, Luke Krstic, Miroslav Shi, Yuanyuan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_20367 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Delay-adaptive Control of Nonlinear Systems with Approximate Neural Operator Predictors Bhan, Luke Krstic, Miroslav Shi, Yuanyuan Systems and Control Machine Learning Dynamical Systems 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. |
| title | Delay-adaptive Control of Nonlinear Systems with Approximate Neural Operator Predictors |
| topic | Systems and Control Machine Learning Dynamical Systems |
| url | https://arxiv.org/abs/2508.20367 |