Verifiable Error Bounds for Physics-Informed Neural KKL Observers
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.
| Authors | Hannah Berin-Costain, Harry Wang, Kirsten Morris et al. |
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| Primary category | eess.SY |
| Published | 20 March 2026 |
| Last updated at source | 20 March 2026 |
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