POD-based feedback control of the Burgers equation by solving the evolutionary HJB equation

被引：28
作者：
Kunisch, K [1 ]
Xie, L [1 ]
机构：
[1] Karl Franzens Univ Graz, Inst Math, A-8010 Graz, Austria
来源：
COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2005年 / 49卷 / 7-8期
关键词：
dynamic programming; Hamilton-Jacobi-Bellman equation; closed loop control; proper orthogonal decomposition; Burgers equation;
D O I：
10.1016/j.camwa.2004.07.022
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A new approach for solving finite-time horizon feedback control problems for distributed parameter systems is proposed. It is based on model reduction by proper orthogonal decomposition combined with efficient numerical methods for solving the resulting low-order evolutionary Hamilton-Jacobi-Bellman (HJB) equation. The feasibility of the proposed methodology is demonstrated by means of optimal feedback control for the Burgers equation. The method for solving the HJB equation is first tested on several 1-D problems and then successfully applied to the control of the reduced order Burgers equation. The effect of noise is investigated, and parallelism is used for computational speedup. (c) 2005 Elsevier Ltd. All rights reserved.
引用
收藏
页码：1113 / 1126
页数：14
相关论文
共 22 条
  • [1] [Anonymous], 1997, Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations
  • [2] Proper orthogonal decomposition for reduced basis feedback controllers for parabolic equations
    Atwell, JA
    King, BB
    [J]. MATHEMATICAL AND COMPUTER MODELLING, 2001, 33 (1-3) : 1 - 19
  • [3] Feedback control methodologies for nonlinear systems
    Beeler, SC
    Tran, HT
    Banks, HT
    [J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2000, 107 (01) : 1 - 33
  • [4] Berkooz G., 1996, Turbulence, Coherent Structures, Dynamical Systems and symmetry
  • [5] Dautray R., 1992, Mathematical Analysis and Numerical Methods for Science and Technology, V5
  • [6] FURLANI T, INTRO PARALLEL COMPU
  • [7] GOTTLIEB S, 1996, 9650 ICASE
  • [8] HEIBERG E, MATLAB PARALLIZATION
  • [9] HUANG CS, SOLVING HAMILTON JAC
  • [10] Reduced order feedback synthesis for viscous incompressible flows
    Ito, K
    Schroeter, JD
    [J]. MATHEMATICAL AND COMPUTER MODELLING, 2001, 33 (1-3) : 173 - 192
123