On the Boundary Control of a Boussinesq System (Journal of Informatics and Mathematical Sciences, 2020)
A boundary control problem is considered for determining a canal depth function optimally for a canal system modeled by a nonlinear Boussinesq equation. By determining the optimal canal depth function, it is aimed to damp out the undesired waves in canal system filled up water. For achieving this aim, the existence and uniqueness of the solutions to system and controllability properties of the system is investigated. Optimal canal depth control function is obtained by means of a maximum principle, which is an elegant tool for transferring the optimal boundary control problem to solving a system of equations including initial-terminal-boundary conditions. The reason making this paper is important that optimal control function is gained without linearization of nonlinear term in the system. In order to show the correctness of the obtained theoretical results, several numerical examples are presented by MATLAB in graphical and table forms. Observing these tables and graphics, it is concluded that introduced boundary control algorithm is effective and has the potential for extending to other nonlinear control systems.
Keywords: Wellposedness; Boussinesq; Canal; Hamiltonian