The Regulator Problem to the Convection–Diffusion Equation

Andrés A. Ramírez and Francisco Jurado ()
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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

Mathematics, 2023, vol. 11, issue 8, 1-16

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.

Keywords: convection–diffusion equation; disturbance rejection; exogenous system; regulator problem; semigroup theory; Sturm–Liouville differential operator; tracking (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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