Nonlinear Boundary Control of the Generalized Burgers Equation

Abstract

In this paper, the adaptive and non-adaptive stabilization of the generalized Burgers equation by nonlinear boundary control are analyzed. For the non-adaptive case, we show that the controlled system is exponentially stable in L2. As for the adaptive case, we present a novel and elegant approach to show the L2 regulation of the solution of the generalized Burgers system. Numerical results supporting and reinforcing the analytical ones of both the controlled and uncontrolled system for the non-adaptive and adaptive cases are presented using the Chebychev collocation method with backward Euler method as a temporal scheme.