Optimal control of two-dimensional parabolic partial differential equations with application to steel billets cooling in continuous casting secondary cooling zone

Optimal control of two-dimensional parabolic partial differential equations with application to steel billets cooling in continuous casting secondary cooling zone

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Article ID: iaor20163926
Volume: 37
Issue: 6
Start Page Number: 1314
End Page Number: 1328
Publication Date: Nov 2016
Journal: Optimal Control Applications and Methods
Authors: , , ,
Keywords: optimization, engineering
Abstract:

Our work is devoted to an optimal control problem for two‐dimensional parabolic partial differential equations(PDEs) and its application in engineering sciences. An adjoint problem approach is used for analysis of the Fréchet gradient of the cost functional, and we prove the gradient is Lipschitz continuous. An improved conjugate gradient method is proposed to solve this problem. Based on Lipschitz continuity of the gradient, the convergence analysis of the conjugate gradient algorithm we proposed is studied. Results of some computational experiments obtained by the conjugate gradient algorithm are illustrated. The results show that the improved conjugate gradient algorithm is effective

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