Active control of an improved Boussinesq system

Abstract

In this paper, optimal control of excessive water waves in a canal system, modeled by a nonlinear improved Boussinesq equation, is considered. For this aim, well-posedness and controllability properties of the system is investigated. Suppressing of the waves in the canal system is successfully obtained by means of optimally determining of canal depth control function via maximum principle, which transforms to optimal control problem to solving an nonlinear initial-boundary-terminal value problem. The beauty of the present paper than other studies existing in the literature is that optimal canal depth control function is analytically obtained without linearization of nonlinear term. In order to show effectiveness and robustness of the control actuation, several numerical examples are given by MATLAB in tables and graphical forms.

Analytical and Numerical Results on Global Dynamics of the Generalized Boussinesq Equation with Cubic Nonlinearity and External Excitation

“…Wang and Su [13] studied the finite time blow-up and solvability of solutions in all space dimensions for the Cauchy problem of a Boussinesq equation with dissipation. Yildirim analyzed, theoretically and numerically, the boundary control problem [14] and active control [15] for the nonlinear Boussinesq system.…”