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The Regulator Problem to the Convection–Diffusion Equation

Author

Listed:
  • Andrés A. Ramírez

    (División de Estudios de Posgrado e Investigación, Tecnológico Nacional de México/I.T. La Laguna, Revolución Blvd. and Instituto Tecnológico de La Laguna Av., Torreón 27000, Mexico)

  • Francisco Jurado

    (División de Estudios de Posgrado e Investigación, Tecnológico Nacional de México/I.T. La Laguna, Revolución Blvd. and Instituto Tecnológico de La Laguna Av., Torreón 27000, Mexico)

Abstract

In this paper, from linear operator, semigroup and Sturm–Liouville problem theories, an abstract system model for the convection–diffusion (C–D) equation is proposed. The state operator for this abstract system model is here defined as given in the form of the Sturm–Liouville differential operator (SLDO) plus an integral term of the same SLDO. Our aim is to achieve the trajectory tracking task in the presence of external disturbances to the C–D equation invoking the regulator problem theory, where the state from a finite-dimensional exosystem is the state to the feedback law. In this context, the regulator (Francis) equations, established from the abstract system model for the C–D equation, here are solved; i.e., the state feedback regulator problem (SFRP) for the C–D system has a solution. Our proposal is validated via numerical simulation results.

Suggested Citation

  • Andrés A. Ramírez & Francisco Jurado, 2023. "The Regulator Problem to the Convection–Diffusion Equation," Mathematics, MDPI, vol. 11(8), pages 1-16, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:8:p:1944-:d:1128585
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    References listed on IDEAS

    as
    1. Francisco Jurado & Andrés A. Ramírez, 2020. "State Feedback Regulation Problem to the Reaction-Diffusion Equation," Mathematics, MDPI, vol. 8(11), pages 1-16, November.
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