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Cluster Computing

, Volume 20, Issue 4, pp 2891–2903 | Cite as

The numerical method for the optimal supporting position and related optimal control for the catalytic reaction system

  • Qiyu Liu
  • Qunxiong ZhuEmail author
  • Xin Yu
  • Zhiqiang Geng
  • Longjin Lv
Article
  • 394 Downloads

Abstract

This paper considers the numerical approximation for the optimal supporting position and related optimal control of a catalytic reaction system with some control and state constraints, which is governed by a nonlinear partial differential equations with given initial and boundary conditions. By the Galerkin finite element method, the original problem is projected into a semi-discrete optimal control problem governed by a system of ordinary differential equations. Then the control parameterization method is applied to approximate the control and reduce the original system to an optimal parameter selection problem, in which both the position and related control are taken as decision variables to be optimized. This problem can be solved as a nonlinear optimization problem by a particle swarm optimization algorithm. The numerical simulations are given to illustrate the effectiveness of the proposed numerical approximation method.

Keywords

Optimal supporting position Optimal control Control parameterization method Catalytic reaction system 

Notes

Acknowledgements

This work was partially supported by the National Natural Science Foundation of China (Grant No. 61374096), and the Natural Science Foundation of Zhejiang (Grant No. LY17A010020).

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • Qiyu Liu
    • 1
    • 2
  • Qunxiong Zhu
    • 1
    Email author
  • Xin Yu
    • 2
  • Zhiqiang Geng
    • 1
  • Longjin Lv
    • 2
  1. 1.College of Information Science and TechnologyBeijing University of Chemical TechnologyBeijingChina
  2. 2.Ningbo Institute of TechnologyZhejiang UniversityNingboChina

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