| Issue |
Math. Model. Nat. Phenom.
Volume 15, 2020
|
|
|---|---|---|
| Article Number | 58 | |
| Number of page(s) | 14 | |
| DOI | https://doi.org/10.1051/mmnp/2020024 | |
| Published online | 26 November 2020 | |
Active control of an improved Boussinesq system
Mus Alparslan University,
Mus, Turkey.
* Corresponding author: k.yildirim@alparslan.edu.tr
Received:
19
May
2020
Accepted:
22
June
2020
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.
Mathematics Subject Classification: 76BXX / 34K35 / 47N70 / 14G40
Key words: Boussinesq / maximum principle / water waves / Hamiltonian
© The authors. Published by EDP Sciences, 2020
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