Fractional vs. Ordinary Control Systems: What Does the Fractional Derivative Provide?

J. Alberto Conejero, Jonathan Franceschi and Enric Picó-Marco
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J. Alberto Conejero: Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, 46022 Valencia, Spain
Jonathan Franceschi: Department of Mathematics “F. Casorati”, Università degli Studi di Pavia, 27100 Pavia, Italy
Enric Picó-Marco: Departamento de Ingeniería de Sistemas y Automática, Universitat Politècnica de València, 46022 Valencia, Spain

Mathematics, 2022, vol. 10, issue 15, 1-18

Abstract: The concept of a fractional derivative is not at all intuitive, starting with not having a clear geometrical interpretation. Many different definitions have appeared, to the point that the need for order has arisen in the field. The diversity of potential applications is even more overwhelming. When modeling a problem, one must think carefully about what the introduction of fractional derivatives in the model can provide that was not already adequately covered by classical models with integer derivatives. In this work, we present some examples from control theory where we insist on the importance of the non-local character of fractional operators and their suitability for modeling non-local phenomena either in space (action at a distance) or time (memory effects). In contrast, when we encounter completely different nonlinear phenomena, the introduction of fractional derivatives does not provide better results or further insight. Of course, both phenomena can coexist and interact, as in the case of hysteresis, and then we would be dealing with fractional nonlinear models.

Keywords: fractional-order model; fractional systems; non-linear systems; complex systems; structural properties; identification for control process (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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