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Predefined-time control of distributed-order systems

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Abstract

Distributed-order calculus can be understood as a further generalisation of integer- and fractional-order calculus. Such a general case allows the modelling and understanding of a more extensive engineering and physical systems class. This paper proposes a controller design that enforces the predefined-time convergence of the solution of a distributed-order dynamical system. Besides, a predefined-time sliding mode design for a general class of uncertain distributed-order dynamical system is proposed. A numerical study is presented to show the reliability of the proposed scheme.

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The present research received no specific grant from any funding agency.

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Authors and Affiliations

  1. College of Engineering, Texas A&M University, Higher Education Center at McAllen, 6200 Tres Lagos Blvd., McAllen, Texas, 78504, USA

    Aldo Jonathan Muñoz-Vázquez

  2. Department of Mathematics and Physics, ITESO, Manuel Gomez Morin 8585 ,Santa Maria Tequepexpan, 45601, San Pedro Tlaquepaque, Jalisco, México

    Juan Diego Sánchez-Torres

  3. Department of Physics and Mathematics, Universidad Iberoamericana, Prol. Paseo de la Reforma 880, Lomas de Santa Fe, Álvaro Obregón, 01219 Mexico City, México

    Guillermo Fernández-Anaya & Fidel Meléndez-Vázquez

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  1. Aldo Jonathan Muñoz-Vázquez
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  2. Guillermo Fernández-Anaya
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  3. Juan Diego Sánchez-Torres
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  4. Fidel Meléndez-Vázquez
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Contributions

A.J. Muñoz-Vázquez: Writing original draft, editing and reviewing, investigation, simulation programming, formal analysis, methodology, conceptualisation, supervision. G. Fernández-Anaya: Writing original draft, editing and reviewing, investigation, formal analysis, methodology, conceptualisation, supervision. J.D. Sánchez-Torres: Writing original draft, editing and reviewing, investigation, formal analysis, methodology, conceptualisation. F. Meléndez-Vázquez: Editing and reviewing, investigation, formal analysis.

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Correspondence to Aldo Jonathan Muñoz-Vázquez.

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Muñoz-Vázquez, A.J., Fernández-Anaya, G., Sánchez-Torres, J.D. et al. Predefined-time control of distributed-order systems. Nonlinear Dyn 103, 2689–2700 (2021). https://doi.org/10.1007/s11071-021-06264-y

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