A virtual control concept for state constrained optimal control problems

被引：13
|
作者：
Krumbiegel, K. [1 ]
Roesch, A. [1 ]
机构：
[1] Austrian Acad Sci, Johann Radon Inst Computat & Appl Math RICAM, A-4040 Linz, Austria
来源：
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS | 2009年 / 43卷 / 02期
基金：
奥地利科学基金会;
关键词：
Optimal control; Elliptic equation; State constraints; Boundary control; Regularization; Virtual control; EQUATIONS;
D O I：
10.1007/s10589-007-9130-0
中图分类号：
C93 [管理学]; O22 [运筹学];
学科分类号：
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要：
A linear elliptic control problem with pointwise state constraints is considered. These constraints are given in the domain. In contrast to this, the control acts only at the boundary. We propose a general concept using virtual control in this paper. The virtual control is introduced in objective, state equation, and constraints. Moreover, additional control constraints for the virtual control are investigated. An error estimate for the regularization error is derived as main result of the paper. The theory is illustrated by numerical tests.
引用
收藏
页码：213 / 233
页数：21
相关论文
共 50 条
  • [41] The control parameterization enhancing transform for constrained optimal control problems
    Teo, KL
    Jennings, LS
    Lee, HWJ
    Rehbock, V
    JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES B-APPLIED MATHEMATICS, 1999, 40 : 314 - 335
  • [42] Tikhonov regularization of control-constrained optimal control problems
    Nikolaus von Daniels
    Computational Optimization and Applications, 2018, 70 : 295 - 320
  • [43] Tikhonov regularization of control-constrained optimal control problems
    von Daniels, Nikolaus
    COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 2018, 70 (01) : 295 - 320
  • [44] Transfer of the Bryson-Denham-Dreyfus Approach for State-constrained ODE Optimal Control Problems to Elliptic Optimal Control Problems
    Frey, Michael
    Bechmann, Simon
    Rund, Armin
    Pesch, Hans Josef
    2011 16TH INTERNATIONAL CONFERENCE ON METHODS AND MODELS IN AUTOMATION AND ROBOTICS, 2011, : 33 - 33
  • [45] NONLINEARLY CONSTRAINED OPTIMAL-CONTROL PROBLEMS
    TEO, KL
    WONG, KH
    JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES B-APPLIED MATHEMATICS, 1992, 33 : 507 - 530
  • [46] A canonical structure for constrained optimal control problems
    Chen, J
    Nett, CN
    Gu, GX
    Xiong, DP
    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, 1996, 6 (07) : 727 - 741
  • [47] A multigrid method for constrained optimal control problems
    Engel, M.
    Griebel, M.
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2011, 235 (15) : 4368 - 4388
  • [48] A NUMERICAL ALGORITHM FOR CONSTRAINED OPTIMAL CONTROL PROBLEMS
    Zhao, Bowen
    Xu, Honglei
    Teo, Kok Lay
    JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION, 2023, 19 (12) : 8602 - 8616
  • [49] Generalized Regularization of Constrained Optimal Control Problems
    Heidrich, Casey R.
    Sparapany, Michael J.
    Grant, Michael J.
    JOURNAL OF SPACECRAFT AND ROCKETS, 2022, 59 (04) : 1096 - 1110
  • [50] Galerkin Optimal Control for Constrained Nonlinear Problems
    Boucher, Randy
    Kang, Wei
    Gong, Qi
    2014 AMERICAN CONTROL CONFERENCE (ACC), 2014, : 2432 - 2437
12345