The paper presents a novel differentiator that addresses the limitations of existing approaches. The key highlights are:
The differentiator is robust and exact, meaning it can recover the signal's derivative from noisy measurements, and its output converges to the true derivative in the absence of noise.
It achieves the optimal worst-case differentiation error, which is not shared by other existing differentiators.
The differentiator's output is Lipschitz continuous, allowing for a smooth derivative estimate. The Lipschitz constant can be tuned as a trade-off between convergence speed and output smoothness.
Both continuous-time and sample-based (discrete-time) versions of the differentiator are developed, with theoretical guarantees established for both.
The continuous-time version consists of a regularized and sliding-mode-filtered linear adaptive differentiator, while the sample-based version is obtained through appropriate discretization.
An illustrative example is provided to highlight the features of the developed differentiator, including its superior performance compared to existing approaches.
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by Rodrigo Alda... في arxiv.org 04-10-2024
https://arxiv.org/pdf/2404.05863.pdfاستفسارات أعمق