Adaptive Boundary Control of the Forced Generalized Kortewegde Vries-Burgers Equation

Smaoui, Nejib; El-Kadri, Alaa; Zribi, Mohamed

doi:10.3166/ejc.16.72-84

Cited by 12 publications

(9 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…is equation is useful in modeling many physical phenomena such as the unidirectional propagation of planar waves [33], strain waves and longitudinal deformation in a nonlinear elastic rod [34], and pressure waves in a liquid-gas bubble mixture [5]. Note that there has been a growing interest in the analysis and control of the GKdVB equation [2,33,[35][36][37][38][39][40][41]. Specifically, long-time behavior of periodic solutions of the GKdVB equation has been investigated [2].…”

Section: Introductionmentioning

confidence: 99%

“…Later on, Smaoui et al [40] designed three different nonadaptive boundary control laws, when α is a positive real number, and showed numerically for certain values of α that the proposed controllers outperform those designed in [38]. On the other hand, the adaptive boundary control of the GKdVB equation was discussed in [39,42] when either the kinematic viscosity ν or the dynamic viscosity µ is unknown or when both viscosities ] and µ are unknown.…”

Section: Introductionmentioning

confidence: 99%

“…Up to our knowledge, the adaptive boundary stabilization problem of the MGKdVB equation has not been examined in the literature. In fact, as previously discussed, the adaptive control stabilization of the MGKdVB equation (1) has been dealt with in the following specific cases: μ � c 2 � 0 in [9,12,14,15], c 2 � 0 in [39,42], and μ � 0 in [24].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Nonlinear Adaptive Boundary Control of the Modified Generalized Korteweg–de Vries–Burgers Equation

2020

View full text Add to dashboard Cite

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 ν, 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.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Nonlinear Adaptive Boundary Control of the Modified Generalized Korteweg–de Vries–Burgers Equation

2020

View full text Add to dashboard Cite

show abstract

“…When γ 1 = 1 and γ 2 = 0 in Eq. (1), the MGKdVB equation gives the generalized Korteweg-de Vries-Burgers (GKdVB) equation; the non-adaptive and adaptive control problems of this equation were studied by Smaoui and Jamal [30] and Smaoui et al [31][32][33].…”

Section: Introductionmentioning

confidence: 99%

Modelling and nonlinear boundary stabilization of the modified generalized Korteweg–de Vries–Burgers equation

2019

View full text Add to dashboard Cite

In this paper, we study the modelling and nonlinear boundary stabilization problem of the modified generalized Korteweg-de Vries-Burgers equation (MGKdVB) when the spatial domain is [0, 1]. First, the MGKdVB equation is derived using the long-wave approximation and perturbation method. Then, two nonlinear boundary controllers are proposed for this equation and the L 2 -global exponential stability of the solution is shown. Numerical simulations are given to illustrate the efficiency of the developed control schemes.

show abstract

“…It also models longitudinal deformations in nonlinear elastic rod [26]. The non-adaptive and adaptive control problems of this equation were studied in [37] and [38,39].…”

Section: Introductionmentioning

confidence: 99%

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

2019

Self Cite

View full text Add to dashboard Cite

The linear stabilization problem of the modified generalized Korteweg-de Vries-Burgers equation (MGKdVB) is considered when the spatial variable lies in [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). 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.

show abstract

Adaptive Boundary Control of the Forced Generalized Kortewegde Vries-Burgers Equation

Cited by 12 publications

References 20 publications

Nonlinear Adaptive Boundary Control of the Modified Generalized Korteweg–de Vries–Burgers Equation

Nonlinear Adaptive Boundary Control of the Modified Generalized Korteweg–de Vries–Burgers Equation

Modelling and nonlinear boundary stabilization of the modified generalized Korteweg–de Vries–Burgers equation

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

Contact Info

Product

Resources

About