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Journal of Industrial and Management Optimization (JIMO)
 

Time delayed optimal control problems with multiple characteristic time points: Computation and industrial applications

Pages: 705 - 718, Volume 5, Issue 4, November 2009      doi:10.3934/jimo.2009.5.705

 
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Ling Yun Wang - School of Information Science and Engineering, Central South University, Changsha 410083, China (email)
Wei Hua Gui - School of Information Science and Engineering, Central South University, Changsha 410083, China (email)
Kok Lay Teo - Department of Mathematics and Statistics, Curtin University, G.P.O. Box U1987, Perth, WA 6845, Australia (email)
Ryan Loxton - Department of Mathematics and Statistics, Curtin University, Perth 6845, Australia (email)
Chun Hua Yang - School of Information Science and Engineering, Central South University, Changsha 410083, China (email)

Abstract: In this paper, we consider a class of optimal control problems involving time delayed dynamical systems and subject to continuous state inequality constraints. We show that this type of problem can be approximated by a sequence of time delayed optimal control problems subject to inequality constraints in canonical form and with multiple characteristic time points appearing in the cost and constraint functions. We derive formulae for the gradient of the cost and constraint functions of the approximate problems. On this basis, each approximate problem can be solved using a gradient-based optimization technique. The computational method obtained is then applied to an industrial problem arising in the study of purification process of zinc sulphate electrolyte. The results are highly satisfactory.

Keywords:  Time delayed system, multiple characteristic time points, continuous state inequality constraints, optimal control, zinc sulphate electrolyte, purification process.
Mathematics Subject Classification:  Primary: 49J15, 49N90; Secondary: 62P30.

Received: October 2008;      Revised: March 2009;      Available Online: August 2009.