This paper addresses the problem of estimating multiplicative fault signals in linear time-invariant systems by processing its input and output variables, as well as designing an input signal to maximize the accuracy of such estimates. The proposed real-time fault estimator is based on a residual generator used for fault detection and a multiple-output regressor generator, which feed a moving-horizon linear regression that estimates the parameter changes. Asymptotic performance guarantees are provided in the presence of noise. Motivated by the performance bounds, an optimal input design problem is formulated, for which we provide efficient algorithms and optimality bounds. Numerical examples demonstrate the efficacy of our approach and the importance of the optimal input design for accurate fault estimation.
@article{arxiv.2506.23769,
title = {Active Estimation of Multiplicative Faults in Dynamical Systems},
author = {Gabriel de Albuquerque Gleizer and Peyman Mohajerin Esfahani and Tamas Keviczky},
journal= {arXiv preprint arXiv:2506.23769},
year = {2025}
}