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Dual strategy for 2‐dimensional PDE optimal control problem in the reheating furnace
Author(s) -
Luo Xiaochuan,
Yang Zhi
Publication year - 2017
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.2386
Subject(s) - conjugate gradient method , slab , dual (grammatical number) , lipschitz continuity , mathematical optimization , partial differential equation , mathematics , temperature gradient , optimal control , heat transfer , gradient method , adjoint equation , optimization problem , computer science , mathematical analysis , mechanics , physics , engineering , structural engineering , art , literature , quantum mechanics
Summary In this paper, the dual strategy is used to solve the 2‐dimensional partial differential equation optimal control problem by introducing the adjoint problem approach to the optimization model. It is proved that the Fr é chet gradient of the cost functional could be written via the weak solution of the adjoint problem, and then, Lipschitz continuity of the gradient is derived. An improved conjugate gradient algorithm is used to solve this problem. Then, the proposed method is applied to obtain the reference values of the optimal furnace zone temperatures and achieve the desired temperature for steel slabs in the reheating furnace. Model validation and comparison between the mathematical model and the experiment results indicate that the present heat transfer model works well for the prediction of thermal behavior about the slab in the reheating furnace. Results of some computational experiments in the simulations of the A3 slab are illustrated, which verifies the effectiveness of the proposed method.