# Dual strategy for 2‐dimensional PDE optimal control problem in the reheating furnace

Dual strategy for 2‐dimensional PDE optimal control problem in the reheating furnace 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 échet 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Optimal Control Applications and Methods Wiley

# Dual strategy for 2‐dimensional PDE optimal control problem in the reheating furnace

, Volume 39 (2) – Jan 1, 2018
16 pages

/lp/wiley/dual-strategy-for-2-dimensional-pde-optimal-control-problem-in-the-zvFBqwPFTi
Publisher
Wiley Subscription Services, Inc., A Wiley Company
ISSN
0143-2087
eISSN
1099-1514
D.O.I.
10.1002/oca.2386
Publisher site
See Article on Publisher Site

### Abstract

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 échet 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.

### Journal

Optimal Control Applications and MethodsWiley

Published: Jan 1, 2018

Keywords: ; ; ; ;

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