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• W3217685280 abstract "The problem of differentiating a function with bounded second derivative in the presence of bounded measurement noise is considered in both continuous-time and sampled-data settings. Fundamental performance limitations of causal differentiators, in terms of the smallest achievable worst-case differentiation error, are shown. A robust exact differentiator is then constructed via the adaptation of a single parameter of a linear differentiator. It is demonstrated that the resulting differentiator exhibits a combination of properties that outperforms existing continuous-time differentiators: it is robust with respect to noise, it instantaneously converges to the exact derivative in the absence of noise, and it attains the smallest possible -- hence optimal -- upper bound on its differentiation error under noisy measurements. For sample-based differentiators, the concept of quasi-exactness is introduced to classify differentiators that achieve the lowest possible worst-case error based on sampled measurements in the absence of noise. A straightforward sample-based implementation of the proposed linear adaptive continuous-time differentiator is shown to achieve quasi-exactness after a single sampling step as well as a theoretically optimal differentiation error bound that, in addition, converges to the continuous-time optimal one as the sampling period becomes arbitrarily small. A numerical simulation illustrates the presented formal results." @default.
• W3217685280 created "2021-12-06" @default.
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• W3217685280 date "2023-02-01" @default.
• W3217685280 modified "2023-10-06" @default.
• W3217685280 title "Optimal robust exact differentiation via linear adaptive techniques" @default.
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• W3217685280 doi "https://doi.org/10.1016/j.automatica.2022.110725" @default.
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