Nonlinear Adaptive Boundary Control of the Modified Generalized Korteweg–de Vries–Burgers Equation. (9th January 2020)

• Record Type: Journal Article
• Authors: Chentouf, B.; Smaoui, N.; Alalabi, A.
• Other Names: Volchenkov Dimitri Academic Editor.
• Is Part Of: Complexity. Volume 2020(2020)
• Publication Date: 2020-01-09
• Subjects: Chaotic behavior in systems -- Periodicals; Complexity (Philosophy) -- Periodicals; 003
• DOI: 10.1155/2020/4574257
• Languages: English
• ISSNs: 1076-2787

Abstract

Abstract : 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, γ 1, and γ 2 and depending whether these parameters are known or unknown. Then, using Lyapunov theory, the L 2 -global exponential stability of the solution is proven in each case. Finally, numerical simulations are presented to illustrate the developed control schemes.