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OPTIMAL CONTROL OF MULTIPLE-TIME DELAYED SYSTEMS BASED ON THE CONTROL PARAMETERIZATION METHOD

Part of: Existence theories

Published online by Cambridge University Press:  29 May 2012

W. H. GUI ,
X. Y. SHEN ,
N. CHEN ,
C. H. YANG  and
L. Y. WANG
W. H. GUI
Affiliation:
School of Information Science and Engineering, Central South University, Changsha, 410083, PR China (email: gwh@csu.edu.cn, shxy-0501@163.com, ningchen@csu.edu.cn, ychh@csu.edu.cn)
X. Y. SHEN
Affiliation:
School of Information Science and Engineering, Central South University, Changsha, 410083, PR China (email: gwh@csu.edu.cn, shxy-0501@163.com, ningchen@csu.edu.cn, ychh@csu.edu.cn)
N. CHEN*
Affiliation:
School of Information Science and Engineering, Central South University, Changsha, 410083, PR China (email: gwh@csu.edu.cn, shxy-0501@163.com, ningchen@csu.edu.cn, ychh@csu.edu.cn)
C. H. YANG
Affiliation:
School of Information Science and Engineering, Central South University, Changsha, 410083, PR China (email: gwh@csu.edu.cn, shxy-0501@163.com, ningchen@csu.edu.cn, ychh@csu.edu.cn)
L. Y. WANG
Affiliation:
School of Electrical Engineering and Renewable Energy, China Three Gorges University, Yichang, 443002, PR China (email: wly@ctgu.edu.cn)
*
✉For correspondence; e-mail: ningchen@csu.edu.cn
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Abstract

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In this paper we study optimal control computation based on the control parameterization method for a class of optimal control problems involving nonlinear systems with multiple time delays subject to continuous state inequality constraints. Both the state and the control are allowed to have different time delays, and they are uncorrelated in this system. The control of the dynamical system is approximated by a piecewise constant function whose heights are taken as decision vectors. The formulae for computing the gradients of the cost and constraint functions are then derived. Based on this, a computational method for finding the optimal control is developed by utilizing the Sequential Quadratic Programming (SQP) algorithm with an active set strategy. The computational method is applied to an industrial problem arising in the purification process of zinc hydrometallurgy. Numerical simulation shows that the amount of zinc powder that is needed can be decreased significantly, thus avoiding wastage of resources.

Keywords

multiple-time delayed systemcontrol parameterizationcontinuous state inequality constraintsSQP algorithm

MSC classification

Secondary: 49J15: Optimal control problems involving ordinary differential equations
Type
Research Article
Information
The ANZIAM Journal , Volume 53 , Issue 1 , July 2011 , pp. 68 - 86
Copyright
Copyright © Australian Mathematical Society 2012

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