An Exact Robust Differentiator Based on Continuous Fractional Sliding Modes

• 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 f(over dot)(t), of f(t), by assuming the boundedness of its second-order derivative, f(over double dot)(t), but it has been pointed out that if f(over dot)(t) is casted as a Holder function, then fotthorn is continuous but not necessarily differentiable, and as a consequence, the existence of f(over dot)(t) 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 f(over dot)(t), even if fotthorn does not exist. A numerical study is discussed to show the reliability of the proposed scheme.

Ämnesord

TEKNIK OCH TEKNOLOGIER  -- Elektroteknik och elektronik -- Reglerteknik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Electrical Engineering, Electronic Engineering, Information Engineering -- Control Engineering (hsv//eng)

Nyckelord

robust exact differentiator

fractional sliding modes

Holder functions

nonlinear systems

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