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October  2009, 5(4): 705-718. doi: 10.3934/jimo.2009.5.705

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

Ling Yun Wang 1, , Wei Hua Gui 1, , Kok Lay Teo 2, , Ryan Loxton 3, and  Chun Hua Yang 1,

1. 

School of Information Science and Engineering, Central South University, Changsha 410083, China, China, China
2. 

Department of Mathematics and Statistics, Curtin University, G.P.O. Box U1987, Perth, WA 6845
3. 

Department of Mathematics and Statistics, Curtin University, Perth 6845, Australia

Received  October 2008 Revised  March 2009 Published  August 2009

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: zinc sulphate electrolyte, purification process., continuous state inequality constraints, optimal control, multiple characteristic time points, Time delayed system.
Mathematics Subject Classification: Primary: 49J15, 49N90; Secondary: 62P3.
Citation: Ling Yun Wang, Wei Hua Gui, Kok Lay Teo, Ryan Loxton, Chun Hua Yang. Time delayed optimal control problems with multiple characteristic time points: Computation and industrial applications. Journal of Industrial and Management Optimization, 2009, 5 (4) : 705-718. doi: 10.3934/jimo.2009.5.705
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