Certified Moving Horizon Estimation for PEM Fuel Cells

Abstract

This paper presents a certified moving horizon estimation (MHE) framework for nonlinear systems affected by bounded disturbances, measurement noise and model mismatch. The estimator combines a discounted MHE formulation with explicit admissible sets and a certification route based on incremental exponential input/output-to-state stability (i-EIOSS) together with tractable LMI conditions. Feasibility of the problem directly provides the weighting matrices (η, P, Q, R) and a contraction rate, yielding an explicit exponential ISS-type error bound. An affine normalization with congruence-based weight transformations is introduced to improve numerical conditioning while preserving the certified constants. The method is applied to the monitoring of a PEM fuel cell, reconstructing the liquid-water saturation from temperature-only measurements. Simulations and experiments on an H–100 stack show accurate state reconstruction and improved robustness relative to an extended Kalman filter.