TY - JOUR
T1 - Nonlinear adaptive boundary control of the modified generalized korteweg-de vries-burgers equation
AU - Chentouf, B.
AU - Smaoui, N.
AU - Alalabi, A.
N1 - Publisher Copyright:
© 2020 B. Chentouf et al.
PY - 2020
Y1 - 2020
N2 - In this paper, we study the nonlinear adaptive boundary control problem of the modified generalized Korteweg-de Vries-Burgers equation (MGKdVB) when the spatial domain is 0,1. Four different nonlinear adaptive control laws are designed for the MGKdVB equation without assuming the nullity of the physical parameters , μ, γ1, and γ2 and depending whether these parameters are known or unknown. Then, using Lyapunov theory, the L2-global exponential stability of the solution is proven in each case. Finally, numerical simulations are presented to illustrate the developed control schemes.
AB - In this paper, we study the nonlinear adaptive boundary control problem of the modified generalized Korteweg-de Vries-Burgers equation (MGKdVB) when the spatial domain is 0,1. Four different nonlinear adaptive control laws are designed for the MGKdVB equation without assuming the nullity of the physical parameters , μ, γ1, and γ2 and depending whether these parameters are known or unknown. Then, using Lyapunov theory, the L2-global exponential stability of the solution is proven in each case. Finally, numerical simulations are presented to illustrate the developed control schemes.
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U2 - 10.1155/2020/4574257
DO - 10.1155/2020/4574257
M3 - Article
AN - SCOPUS:85078352301
SN - 1076-2787
VL - 2020
JO - Complexity
JF - Complexity
M1 - 4574257
ER -