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

This paper considers the adaptive control problem of the forced generalized Korteweg-de Vries-Burgers (GKdVB) equation when the spatial domain is [0,1]. Three different adaptive control laws are designed for the forced GKdVB equation when either the kinematic viscosity ν or the dynamic viscosity μ is unknown, or when both viscosities ν and μ are unknowns. The L2 -global exponential stability of the solutions of these equations is shown for each of the proposed control laws by using the Lyapunov theory. Numerical simulations based on the Finite Element method (FEM) are presented to validate the analytical developments.