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.
Issue Section:
Research Papers
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