Set Point Regulation Control for KdVB Equation

We investigate inverse optimal set point regulation control for Korteweg-de Vries-Burgers (KdVB) equation. For a given set point, we establish boundary controls to regulate state of the closed-loop system to the set point from any initial value. Most of important, we prove that the proposed boundary controls are such that state of the closed-loop system is bounded and converges to the set point. Furthermore, we show that it is optimal to a meaningful functional after making minor modification to the boundary controls. Finally, an example is given to show the effectiveness of the proposed method.