Parallelized POD-based suboptimal economic model predictive control of a state-constrained Boussinesq approximation

Motivated by an energy efficient building application, we want to optimize a quadratic cost functional subject to the Boussinesq approximation of the Navier-Stokes equations and to bilateral state and control constraints. Since the computation of such an optimal solution is numerically costly, we de...

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Bibliographic Details
Published inComputers & mathematics with applications (1987) Vol. 116
Main Authors Andrej, Julian, Grüne, Lars, Mechelli, Luca, Meurer, Thomas, Pirkelmann, Simon, Volkwein, Stefan
Format Journal Article
LanguageEnglish
Published United States Elsevier 29.09.2021
Subjects
Boussinesq approximation
MATHEMATICS AND COMPUTING
Model predictive control
Parallel computing
Proper orthogonal decomposition
State constraints
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ISSN0898-1221
1873-7668

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Summary:Motivated by an energy efficient building application, we want to optimize a quadratic cost functional subject to the Boussinesq approximation of the Navier-Stokes equations and to bilateral state and control constraints. Since the computation of such an optimal solution is numerically costly, we design an efficient strategy to compute a sub-optimal (but applicationally acceptable) solution with significantly reduced computational effort. We employ an economic Model Predictive Control (MPC) strategy to obtain a feedback control. The MPC sub-problems are based on a linear-quadratic optimal control problem subjected to mixed control and state constraints and a convection-diffusion equation, reduced with proper orthogonal decomposition. Finally, to solve each sub-problem, we apply a primal-dual active set strategy. The method can be fully parallelized, which enables the solution of large problems with real-world parameters.
Bibliography:LLNL-JRNL-818244
AC52-07NA27344; LLNL-JRNL-818244
USDOE National Nuclear Security Administration (NNSA)
ISSN:0898-1221
1873-7668