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

Ling Yun Wang; Wei Hua Gui; Kok Lay Teo; Ryan Loxton; Chun Hua Yang

doi:10.3934/jimo.2009.5.705

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2009, Volume 5, Issue 4: 705-718. Doi: 10.3934/jimo.2009.5.705

This issue Previous Article On second order symmetric duality in nondifferentiable multiobjective programming Next Article Random time ruin probability for the renewal risk model with heavy-tailed claims

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

1.
School of Information Science and Engineering, Central South University, Changsha 410083
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

Received: September 30, 2008

Revised: February 28, 2009

Published: September 2009

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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.

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