用神经算子逼近延迟系统控制器，实现快速稳定控制。
Delay-adaptive Control of Nonlinear Systems with Approximate Neural Operator Predictors
- 用可离线训练的神经算子近似预测控制器，提升实时性。
- 理论证明系统在预测误差和延迟范围内半全局实用收敛。
- 在生物反馈系统中实测速度提升15倍，适合复杂延迟系统控制。
本文提出一种严格方法，用于实现具有未知且任意长执行器延迟的非线性系统的预测反馈控制。由于预测器解析不可解，我们采用学习得到的神经算子映射对其进行近似。该映射一次性离线训练后在线部署，利用神经网络的快速推理能力。基于神经算子的通用逼近定理和延迟的传输偏微分方程（PDE）表示，我们通过李雅普诺夫-克拉索夫斯基泛函证明了系统依赖于预测器近似误差和延迟界时的半全局实用收敛性。最后，我们在一个生物激活/抑制系统上验证了理论结果，相比传统数值方法实现了15倍的速度提升。
原文摘要 · Abstract (English)
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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