Nonlinear adaptive boundary control of the modified generalized korteweg-de vries-burgers equation

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.