POD-based augmented Lagrangian method for state constrained heat-convection phenomena
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2018
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Zusammenfassung
We consider an optimal boundary control problem of the heat equation with convection with bilateral control and state constraints. The goal is to keep the temperature (state) within a desired range while the norm of the boundary controls is minimized. To numerically approximate the unique solution of the problem, a first-order augmented Lagrangian method is utilized. The gradient of the augmented Lagrangian is characterized by the solution of the adjoint equation. To decrease the computational time, we apply a reduced-order approach based on proper orthogonal decomposition (POD). To gain a sufficiently accurate approximation, we propose and compare different manners to compute the snapshots and thus the POD basis. Numerical tests compare the efficiency of the proposed strategies.
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510 Mathematik
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Optimal control, model predictive control model reduction, augmented Lagrange method, heat equation
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JEHLE, Jonas Siegfried, Luca MECHELLI, Stefan VOLKWEIN, 2018. POD-based augmented Lagrangian method for state constrained heat-convection phenomenaBibTex
@techreport{Jehle2018PODba-42857,
year={2018},
series={Konstanzer Schriften in Mathematik},
title={POD-based augmented Lagrangian method for state constrained heat-convection phenomena},
number={377},
author={Jehle, Jonas Siegfried and Mechelli, Luca and Volkwein, Stefan},
note={Konferenz: IUTAM Symposium 2018, 22. Mai 2018 - 25. Mai 2018, Stuttgart}
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Konferenz: IUTAM Symposium 2018, 22. Mai 2018 - 25. Mai 2018, Stuttgart
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