为神经网络驱动的物理观测器提供可计算的状态估计误差边界。
Verifiable Error Bounds for Physics-Informed Neural KKL Observers
- 用神经网络验证技术，仅依赖可认证量推导误差界。
- 在非线性系统上实现带噪声测量的可证明状态估计保证。
- 适合关注安全控制与可信机器学习的科研人员。
本文提出一种可计算的状态估计误差边界，用于基于学习的Kazantzis--Kravaris/Luenberger（KKL）观测器。近期工作利用物理信息神经网络（PINN）学习KKL变换映射，并用传统神经网络学习对应左逆映射，但该方法尚无可计算的状态估计误差边界。本文推导出仅依赖在指定区域内可通过神经网络验证认证的量的误差边界，并进一步扩展至存在有界加性测量噪声的情形，在非线性基准系统上验证了其有效性。
原文摘要 · Abstract (English)
This paper proposes a computable state-estimation error bound for learning-based Kazantzis--Kravaris/Luenberger (KKL) observers. Recent work learns the KKL transformation map with a physics-informed neural network (PINN) and a corresponding left-inverse map with a conventional neural network. However, no computable state-estimation error bounds are currently available for this approach. We derive a state-estimation error bound that depends only on quantities that can be certified over a prescribed region using neural network verification. We further extend the result to bounded additive measurement noise and demonstrate the guarantees on nonlinear benchmark systems.
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