Second‐order predefined‐time sliding‐mode control of fractional‐order systems

This paper presents a predefined‐time control of fractional‐order linear system subject to a large class of continuous but not necessarily integer‐order differentiable disturbances. The dynamical system is based on the Caputo derivative and has an order that lies in (1,2). The proposed controller, b...

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Bibliographic Details
Published inAsian journal of control Vol. 24; no. 1; pp. 74 - 82
Main Authors Muñoz‐Vázquez, Aldo Jonathan, Sánchez‐Torres, Juan Diego, Defoort, Michael
Format Journal Article
LanguageEnglish
Published Hoboken Wiley Subscription Services, Inc 01.01.2022
Subjects
Controllers
Disturbances
Dynamical systems
finite‐time stability
fixed‐time stability
fractional‐order systems
Integers
predefined‐time stability
second‐order sliding‐mode control
Sliding mode control
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Summary:This paper presents a predefined‐time control of fractional‐order linear system subject to a large class of continuous but not necessarily integer‐order differentiable disturbances. The dynamical system is based on the Caputo derivative and has an order that lies in (1,2). The proposed controller, based on a dynamic extension, induces an integer‐order reaching phase, such that an invariant second‐order sliding mode is enforced in predefined‐time, that is, the solution of the fractional‐order system and its integer‐order derivative converge to the origin within a time that is prescribed as a tunable control parameter. The controller is continuous and able to compensate for unknown continuous disturbances. A simulation study is carried out in order to show the effectiveness of the proposed scheme.
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ISSN:1561-8625
1934-6093
DOI:10.1002/asjc.2447