Verifiable Error Bounds for Physics-Informed Neural KKL Observers

TL;DR

This paper introduces a method to compute verifiable error bounds for physics-informed neural network-based KKL observers, enabling certified state estimation even with measurement noise on nonlinear systems.

Contribution

It provides the first verifiable, computable error bounds for neural network-based KKL observers, extending to noisy measurements and nonlinear systems.

Findings

Error bounds depend on verifiable neural network quantities

Bounds are applicable to systems with measurement noise

Demonstrated on nonlinear benchmark systems

Abstract

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.