Sequential linear quadratic control of bilinear parabolic PDEs based on POD model reduction

	Sequential linear quadratic control of bilinear parabolic PDEs based on POD model reduction
	Xu Chao; Ou Yongsheng; Schuster Eugenio
刊名	AUTOMATICA
	2011
卷号	47 期号:2 页码:418-426
英文摘要	We present a framework to solve a finite-time optimal control problem for parabolic partial differential equations (PDEs) with diffusivity-interior actuators, which is motivated by the control of the current density profile in tokamak plasmas. The proposed approach is based on reduced order modeling (ROM) and successive optimal control computation. First we either simulate the parabolic PDE system or carry out experiments to generate data ensembles, from which we then extract the most energetic modes to obtain a reduced order model based on the proper orthogonal decomposition (POD) method and Galerkin projection. The obtained reduced order model corresponds to a bilinear control system. Based on quasi-linearization of the optimality conditions derived from Pontryagin’s maximum principle, and stated as a two boundary value problem, we propose an iterative scheme for suboptimal closed-loop control. We take advantage of linear synthesis methods in each iteration step to construct a sequence of controllers. The convergence of the controller sequence is proved in appropriate functional spaces. When compared with previous iterative schemes for optimal control of bilinear systems, the proposed scheme avoids repeated numerical computation of the Riccati equation and therefore reduces significantly the number of ODEs that must be solved at each iteration step. A numerical simulation study shows the effectiveness of this approach.
收录类别	SCI
原文出处	http://www.sciencedirect.com/science/article/pii/S000510981000484X#
语种	英语
内容类型	期刊论文
源URL	[http://ir.siat.ac.cn:8080/handle/172644/3248]
专题	深圳先进技术研究院_集成所
作者单位	AUTOMATICA
推荐引用方式 GB/T 7714	Xu Chao,Ou Yongsheng,Schuster Eugenio. Sequential linear quadratic control of bilinear parabolic PDEs based on POD model reduction[J]. AUTOMATICA,2011,47(2):418-426.
APA	Xu Chao,Ou Yongsheng,&Schuster Eugenio.(2011).Sequential linear quadratic control of bilinear parabolic PDEs based on POD model reduction.AUTOMATICA,47(2),418-426.
MLA	Xu Chao,et al."Sequential linear quadratic control of bilinear parabolic PDEs based on POD model reduction".AUTOMATICA 47.2(2011):418-426.