The problem addressed in this paper is the online differentiation of a signal/function that possesses a continuous but not necessarily differentiable derivative. In the realm of (integer) high-order sliding modes, a continuous differentiator provides the exact estimation of the derivative , of f(t), by assuming the boundedness of its second-order derivative, , but it has been pointed out that if is casted as a Hölder function, then is continuous but not necessarily differentiable, and as a consequence, the existence of is not guaranteed, but even in such a case, the derivative of f(t) can be exactly estimated by means of a continuous fractional sliding mode-based differentiator. Then, the properties of fractional sliding modes, as exact differentiators, are studied. The novelty of the proposed differentiator is twofold: (i) it is continuous, and (ii) it provides the finite-time exact estimation of , even if does not exist. A numerical study is discussed to show the reliability of the proposed scheme.
An Exact Robust Differentiator Based on Continuous Fractional Sliding Modes
Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received December 4, 2017; final manuscript received February 21, 2018; published online April 30, 2018. Assoc. Editor: Hashem Ashrafiuon.
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Jonathan Muñoz-Vázquez, A., Vázquez-Aguilera, C., Parra-Vega, V., and Sánchez-Orta, A. (April 30, 2018). "An Exact Robust Differentiator Based on Continuous Fractional Sliding Modes." ASME. J. Dyn. Sys., Meas., Control. September 2018; 140(9): 091018. https://doi.org/10.1115/1.4039487
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