Set-point Boundary Control for a Viscous Burgers Equation

2005 ◽  
pp. 43-60 ◽  
Author(s):  
C.I. Byrnes ◽  
D.S. Gilliam ◽  
A. Isidori ◽  
V.I. Shubov
Keyword(s):  
Boundary Control ◽  
Burgers Equation ◽  
Point Boundary ◽  
Set Point

Boundary control of MKdV-Burgers equation

2006 ◽  
Vol 27 (1) ◽  
pp. 109-116 ◽  
Author(s):  
Li-xin Tian ◽  
Zhi-feng Zhao ◽  
Jing-feng Wang
Keyword(s):  
Boundary Control ◽  
Burgers Equation

scholarly journals Boundary linear stabilization of the modified generalized Korteweg–de Vries–Burgers equation

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Nejib Smaoui ◽  
Boumediène Chentouf ◽  
Ala’ Alalabi
Keyword(s):  
Exponential Stability ◽  
Numerical Simulations ◽  
Boundary Control ◽  
Existence And Uniqueness ◽  
Burgers Equation ◽  
Global Solutions ◽  
Spatial Variable ◽  
Stabilization Problem ◽  
De Vries ◽  
Adaptive Boundary Control

Abstract The linear stabilization problem of the modified generalized Korteweg–de Vries–Burgers equation (MGKdVB) is considered when the spatial variable lies in $[0,1]$ [ 0 , 1 ] . First, the existence and uniqueness of global solutions are proved. Next, the exponential stability of the equation is established in $L^{2} (0,1)$ L 2 ( 0 , 1 ) . Then, a linear adaptive boundary control is put forward. Finally, numerical simulations for both non-adaptive and adaptive problems are provided to illustrate the analytical outcomes.

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