Parallelized POD-based suboptimal economic model predictive control of a state-constrained Boussinesq approximation. (English) Zbl 1524.65506
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. 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.
MSC:
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 35J20 | Variational methods for second-order elliptic equations |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
| 49K20 | Optimality conditions for problems involving partial differential equations |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 76M20 | Finite difference methods applied to problems in fluid mechanics |
| 65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 93B25 | Algebraic methods |
| 65Y05 | Parallel numerical computation |
| 80A19 | Diffusive and convective heat and mass transfer, heat flow |
| 49M41 | PDE constrained optimization (numerical aspects) |
Keywords:
Boussinesq approximation; model predictive control; state constraints; proper orthogonal decomposition; parallel computingReferences:
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