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

2010 ◽  
Vol 16 (1) ◽  
pp. 72-84 ◽  
Author(s):  
Nejib Smaoui ◽  
Alaa El-Kadri ◽  
Mohamed Zribi
Keyword(s):  
Boundary Control ◽  
Burgers Equation ◽  
Adaptive Boundary Control

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.

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

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-18 ◽  
Author(s):  
B. Chentouf ◽  
N. Smaoui ◽  
A. Alalabi
Keyword(s):  
Boundary Control ◽  
Burgers Equation ◽  
Lyapunov Theory ◽  
Physical Parameters ◽  
Control Laws ◽  
Nonlinear Adaptive Control ◽  
Control Schemes ◽  
De Vries ◽  
Adaptive Boundary Control ◽  
Stability Of The Solution

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.

scholarly journals Weighted multiple model adaptive boundary control for a flexible manipulator

2019 ◽  
Vol 103 (1) ◽  
pp. 003685041988646
Author(s):  
Weicun Zhang ◽  
Qing Li ◽  
Yuzhen Zhang ◽  
Ziyi Lu ◽  
Cheng Nian
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Boundary Control ◽  
Control Strategy ◽  
Flexible Manipulator ◽  
Multiple Model ◽  
Parameter Uncertainties ◽  
Partial Differential ◽  
Local Boundary ◽  
Adaptive Boundary Control

In this article, a weighted multiple model adaptive boundary control scheme is proposed for a flexible manipulator with unknown large parameter uncertainties. First, the uncertainties are approximatively covered by a finite number of constant models. Second, based on Euler–Bernoulli beam theory and Hamilton principle, the distributed parameter model of the flexible manipulator is constructed in terms of partial differential equation for each local constant model. Correspondingly, local boundary controllers are designed to control the manipulator movement and suppress its vibration for each partial differential equation model, which are based on Lyapunov stability theory. Then, a novel weighted multiple model adaptive control strategy is developed based on an improved weighting algorithm. The stability of the overall closed-loop system is ensured by virtual equivalent system theory. Finally, numerical simulations are provided to illustrate the feasibility and effectiveness of the proposed control strategy.

Adaptive boundary control of a vibrating cantilever nanobeam considering small scale effects

2020 ◽  
Vol 105 ◽  
pp. 77-85
Author(s):  
Xinling Yue ◽  
Yuhua Song ◽  
Jianxiao Zou ◽  
We He
Keyword(s):  
Boundary Control ◽  
Scale Effects ◽  
Small Scale ◽  
Adaptive Boundary Control
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