Title: Numerical method for the time optimal control problem governed by the Benjamin-Bona-Mahony equation

Authors: Xin Yu; Qian Zhang; Haolan Zhang; Chao Xu

Addresses: Ningbo Institute of Technology, Zhejiang University, Ningbo, 315100, China ' Ningbo Institute of Technology, Zhejiang University, Ningbo, 315100, China ' Ningbo Institute of Technology, Zhejiang University, Ningbo, 315100, China ' The State Key Laboratory of Industrial Control Technology and Institute of Cyber-Systems and Control, Zhejiang University, Hangzhou, 310027, China

Abstract: This paper deals with the numerical approximation for the time optimal control problem governed by the Benjamin-Bona-Mahony (BBM) equation, which is an unspecified terminal time problem. Firstly, by projecting the original problem with the finite element method (FEM), another approximate problem governed by a system of ordinary differential equations will be obtained. Then, the parameterisation method for the optimal time and the control function will be carried out and the unspecified terminal time problem can be reduced to an optimal parameter selection problem with a fixed time horizon [0, 1]. This optimal parameter selection problem is a standard nonlinear mathematical programming problem and can be solved by sequential quadratic programming (SQP) algorithm. Finally, some numerical simulation studies will be given to illustrate the effectiveness of our numerical approximation method for the time optimal control problem governed by the BBM equation.

Keywords: finite element method; FEM; sequential quadratic programming; SQP; time optimal control; Benjamin-Bona-Mahony equation; BBM; parameterisation; numerical simulation.

DOI: 10.1504/IJCSE.2016.078936

International Journal of Computational Science and Engineering, 2016 Vol.13 No.3, pp.296 - 302

Received: 22 Dec 2013
Accepted: 18 Aug 2014
Published online: 06 Sep 2016 *

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