### Electronic Research Archive

2021, Issue 3: 2533-2552. doi: 10.3934/era.2020128
Special Issues

# Efficient computations for linear feedback control problems for target velocity matching of Navier-Stokes flows via POD and LSTM-ROM

• Received: 01 August 2020 Revised: 01 September 2020 Published: 14 December 2020
• Primary: 76D55, 49M25, 49M41, 68T07; Secondary: 65M60

• An efficient computing method for a target velocity tracking problem of fluid flows is considered. We first adopts the Lagrange multipliers method to obtain the optimality system, and then designs a simple and effective feedback control law based on the relationship between the control ${{\boldsymbol f}}$ and the adjoint variable ${{\boldsymbol w}}$ in the optimality system. We consider a reduced order modeling (ROM) of this problem for real-time computing. In order to improve the existing ROM method, the deep learning technique, which is currently being actively researched, is applied. We review previous research results and some computational results are presented.

Citation: Hyung-Chun Lee. Efficient computations for linear feedback control problems for target velocity matching of Navier-Stokes flows via POD and LSTM-ROM[J]. Electronic Research Archive, 2021, 29(3): 2533-2552. doi: 10.3934/era.2020128

### Related Papers:

• An efficient computing method for a target velocity tracking problem of fluid flows is considered. We first adopts the Lagrange multipliers method to obtain the optimality system, and then designs a simple and effective feedback control law based on the relationship between the control ${{\boldsymbol f}}$ and the adjoint variable ${{\boldsymbol w}}$ in the optimality system. We consider a reduced order modeling (ROM) of this problem for real-time computing. In order to improve the existing ROM method, the deep learning technique, which is currently being actively researched, is applied. We review previous research results and some computational results are presented.

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沈阳化工大学材料科学与工程学院 沈阳 110142

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