Inverse Optimality of Regulation Design for Korteweg-De Vries-Burgers Equation

In optimal control, it is often necessary to solve Hamilton-Jacobi-Isaacs (HJI) partial differential equation, but it is not only difficult to solve, sometimes even impossible to solve. It is possible to avoid solving the HJI equation by using inverse optimal methods. We investigate inverse optimality of regulation design for Korteweg-de Vries-Burgers (KdVB) equation. Two kinds of boundary control laws are achieved to regulate the state of closed-loop system to the set point from any initial value. In order to regulate the convergent speed of the closed-loop system, one or two parameters are designed in the boundary control laws. We proved that boundary control laws are optimal for two meaningful functionals, respectively. The effectiveness of the proposed design has been shown through simulations, and the convergence speed of the closed-loop system accelerates with increase of adjustable parameters.