Next Article in Journal
Analytic Extension of Riemannian Analytic Manifolds and Local Isometries
Next Article in Special Issue
A Meshless Method Based on the Laplace Transform for the 2D Multi-Term Time Fractional Partial Integro-Differential Equation
Previous Article in Journal
Compiled Constructions towards Post-Quantum Group Key Exchange: A Design from Kyber
Previous Article in Special Issue
The Application of Accurate Exponential Solution of a Differential Equation in Optimizing Stability Control of One Class of Chaotic System
Article

Boundary Control for a Certain Class of Reaction-Advection-Diffusion System

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
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(11), 1854; https://doi.org/10.3390/math8111854
Received: 7 September 2020 / Revised: 16 October 2020 / Accepted: 19 October 2020 / Published: 22 October 2020
(This article belongs to the Special Issue Applications of Partial Differential Equations in Engineering)
There are physical phenomena, involving diffusion and structural vibrations, modeled by partial differential equations (PDEs) whose solution reflects their spatial distribution. Systems whose dynamics evolve on an infinite-dimensional Hilbert space, i.e., infinite-dimensional systems, are modeled by PDEs. The aim when designing a controller for infinite-dimensional systems is similar to that for finite-dimensional systems, i.e., the control system must be stable. Another common goal is to design the controller in such a way that the response of the system does not be affected by external disturbances. The controller design for finite-dimensional systems is not an easy task, so, the controller design for infinite-dimensional systems is even more challenging. The backstepping control approach is a dominant methodology for boundary feedback design. In this work, we try with the backstepping design for the boundary control of a reaction-advection-diffusion (R-A-D) equation, namely, a type parabolic PDE, but with constant coefficients and Neumann boundary conditions, with actuation in one of these latter. The heat equation with Neumann boundary conditions is considered as the target system. Dynamics of the open- and closed-loop solution of the PDE system are validated via numerical simulation. The MATLAB®-based numerical algorithm related with the implementation of the control scheme is here included. View Full-Text
Keywords: applied mathematics; backstepping; boundary control; computational methods; distributed parameters system; fluid mechanics; partial differential equations; reaction-advection-diffusion equation applied mathematics; backstepping; boundary control; computational methods; distributed parameters system; fluid mechanics; partial differential equations; reaction-advection-diffusion equation
Show Figures

Figure 1

MDPI and ACS Style

Cruz-Quintero, E.; Jurado, F. Boundary Control for a Certain Class of Reaction-Advection-Diffusion System. Mathematics 2020, 8, 1854. https://doi.org/10.3390/math8111854

AMA Style

Cruz-Quintero E, Jurado F. Boundary Control for a Certain Class of Reaction-Advection-Diffusion System. Mathematics. 2020; 8(11):1854. https://doi.org/10.3390/math8111854

Chicago/Turabian Style

Cruz-Quintero, Eduardo, and Francisco Jurado. 2020. "Boundary Control for a Certain Class of Reaction-Advection-Diffusion System" Mathematics 8, no. 11: 1854. https://doi.org/10.3390/math8111854

Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop