Optimal Robust Exact First-Order Differentiators With Lipschitz-Continuous Output

• 成果类型: Article
• 署名作者: Aldana-Lopez, Rodrigo; Seeber, Richard; Haimovich, Hernan; Gomez-Gutierrez, David
• 署名单位: Intel Corporation; Intel Mexico; Graz University of Technology; Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET); National University of Rosario
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3555481
• 发表日期: 2025
• 页码: 6191-6198
• 关键词: NOISE; accuracy; CONVERGENCE; Robustness; Noise measurement; Tuning; Fault diagnosis; Doppler effect; vibrations; Upper bound; Differentiators; discrete-time implementation; optimal worst-case error; sliding-mode filters

摘要

The signal differentiation problem involves the development of algorithms that allow to recover a signal's derivatives from noisy measurements. This article develops a first-order differentiator with robustness to measurement noise, exactness in the absence of noise, optimal worst-case differentiation error, and Lipschitz-continuous output, where the output's Lipschitz constant is a tunable parameter. This combination of advantageous properties is not shared by any existing differentiator. A sample-based implementation by implicit discretization is obtained, which is quasi-exact, inherits the optimal worst-case error bound, and the Lipschitz constant translates to a discrete-time increment bound. Illustrative examples are provided to highlight the features of the developed differentiator.