On the use of reduced models obtained through identification for feedback optimal control problems in a heat convection–diffusion problem |
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| Authors: | Y Favennec Y Rouizi D Petit |
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| Affiliation: | 1. LTN UMR CNRS 6607, Université de Nantes, Polytech’ Nantes, La chantrerie, 44306 NANTES Cedex 3, France;2. LET UMR CNRS 6608, ENSMA, Téléport 2, 1 avenue Clément Ader, BP 40109, 86961 FUTUROSCOPE Cedex, France;1. Heidelberg Institute for Theoretical Studies, Heidelberg, Germany;2. Department of Ecology and Evolutionary Biology, University of Kansas, Lawrence, KS, USA;3. Biomathematics Research Centre, University of Canterbury, Christchurch, New Zealand;1. Institute of Automatics, National University of San Juan, Av. San Martín 1112 Oeste J5400ARY San Juan, Argentina;2. Department of Systems Engineering and Automatic Control, University of Valladolid, Faculty of Sciences, c/Real de Burgos s/n, 47011 Valladolid, Spain;3. Repsol Petróleo S. A., Refinería de Puertollano, Apartado de Correos 12, 13500 Puertollano, Spain |
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| Abstract: | This paper deals with the use of reduced models for solving some optimal control problems. More precisely, the reduced model is obtained through the modal identification method. The test case which the algorithms is tested on is based on the flow over a backward-facing step. Though the reduction for the velocity fields for different Reynolds numbers is treated elsewhere 1], only the convection–diffusion equation for the energy problem is treated here. The model reduction is obtained through the solution of a gradient-type optimization problem where the objective function gradient is computed through the adjoint-state method. The obtained reduced models are validated before being coupled to optimal control algorithms. In this paper the feedback optimal control problem is considered. A Riccati equation is solved along with the Kalman gain equation. Additionally, a Kalman filter is performed to reconstruct the reduced state through previous and actual measurements. The numerical test case shows the ability of the proposed approach to control systems through the use of reduced models obtained by the modal identification method. |
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