Work

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

Year: 2025

Type: article

Abstract: 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.

Source: IEEE Transactions on Automatic Control

DOI: 10.1109/tac.2025.3555481

Authors: Rodrigo Aldana-López, Richard Seeber, Hernan Haimovich, David Gómez-Gutiérrez

Institutions: Intel (United States), Graz University of Technology, Consejo Nacional de Investigaciones Científicas y Técnicas, National University of Rosario, Centro Internacional Franco-Argentino de Ciencias de la Información y de Sistemas

Language: English

Topic: Control Systems and Identification

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,645

Funders: Österreichische Nationalstiftung für Forschung, Technologie und Entwicklung, Christian Doppler Forschungsgesellschaft, Bundesministerium für Digitalisierung und Wirtschaftsstandort, Agencia Nacional de Promoción de la Investigación, el Desarrollo Tecnológico y la Innovación