Observability and State Estimation for Smooth and Nonsmooth Differential Algebraic Equation Systems
Abstract
In this work, we extend the sensitivity-based rank condition (SERC) test for local observability to another class of systems, namely smooth and nonsmooth differential-algebraic equation (DAE) systems of index-1. The newly introduced test for DAEs, which we call the lexicographic SERC (L-SERC) observability test, utilizes the theory of lexicographic differentiation to compute sensitivity information. Moreover, the newly introduced L-SERC observability test is useful in the context of partial observability as it can judge which states are observable and which are not. Additionally, we introduce a novel sensitivity-based extended Kalman filter (S-EKF) algorithm for state estimation, applicable to both smooth and nonsmooth DAE systems. Finally, we apply the newly developed S-EKF to estimate the states of a wind turbine power system model.
Cite
@article{arxiv.2508.18476,
title = {Observability and State Estimation for Smooth and Nonsmooth Differential Algebraic Equation Systems},
author = {Hesham Abdelfattah and Sameh A. Eisa and Peter Stechlinski},
journal= {arXiv preprint arXiv:2508.18476},
year = {2025}
}