Observability and State Estimation for Smooth and Nonsmooth Differential Algebraic Equation Systems

2025/08/25 by Abdelfattah, Hesham, Eisa, Sameh A., Stechlinski, Peter
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.18476

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.

Citations

• A New Nonsmooth Optimal Control Framework for Wind Turbine Power Systems
• Identifiability and Observability of Nonsmooth Systems via Taylor-like Approximations

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