Verifiable Error Bounds for Physics-Informed Neural KKL Observers
This provides verifiable safety guarantees for state estimation in control systems, though it is incremental as it builds on existing PINN-based observer methods.
The paper tackles the problem of lacking computable state-estimation error bounds for learning-based Kazantzis-Kravaris/Luenberger observers using physics-informed neural networks, and derives a verifiable error bound that can be certified over prescribed regions using neural network verification, demonstrating it on nonlinear benchmark systems.
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.