Computational bilinear optimal control for a class of one-dimensional MHD flow systems. (February 2019)

• Record Type: Journal Article
• Authors: Ren, Zhigang; Zhou, Zhongcheng; Xu, Chao; Wu, Zongze; Chen, Tehuan
• Is Part Of: ISA transactions. Volume 85(2019)
• Page Start: 129
• Page End: 140
• Publication Date: 2019-02
• Subjects: Magnetohydrodynamic -- Flow control -- Galerkin method -- Control parameterization -- Time-scaling transformation -- Bilinear control system; Engineering instruments -- Periodicals; Engineering instruments; Periodicals; Electronic journals; 629.805
• DOI: 10.1016/j.isatra.2018.10.029
• Languages: English
• ISSNs: 0019-0578

Abstract

Abstract: In this paper, we consider a bilinear optimal control problem arising in a one-dimensional (1-D) MHD flow modeled by an array of coupled partial differential equations (PDEs). The external control input (external induction of magnetic field) in the model takes the multiplicative effect on both state variables (i.e., momentum and magnetic components). Our aim is to drive the flow velocity to within close proximity of a desired target flow velocity at the pre-indicated terminal time. We first use the Galerkin method combined with a set of basis quadratic B-spline functions to obtain a semi-discrete approximation problem. Next, the convergence of the semi-discrete approximation problem is proved. Then the control parameterization method combined with the time-scaling transformation technique is utilized to obtain an approximate optimal parameter selection problem, in which the exact gradients of the cost function with respect to the decision parameters are computed based on our analytical equations. The approximate problem are then solved by using the gradient-based optimization techniques such as the sequential quadratic programming (SQP). Finally, the numerical results validate the effectiveness of our method. Highlights: A bilinear optimal control problem arising in a one-dimensional (1D) MHD flow is formulated for tracking a desired target flow velocity. An effective computational optimal control method is developed. The convergence of the semi-discrete approximation optimal control problem is proved rigorously. The exact gradients of the cost functional are computed.