Parallelized POD-based Suboptimal Economic Model Predictive Control of a State-Constrained Boussinesq approximation

TL;DR

This paper introduces a parallelized, reduced-order MPC approach for efficiently controlling a Boussinesq fluid model with constraints, suitable for energy-efficient building applications.

Contribution

It develops a parallelized POD-based suboptimal MPC framework for complex fluid models, reducing computational costs significantly.

Findings

Method achieves substantial computational speed-up.

Enables real-time control of large-scale fluid systems.

Maintains acceptable control performance with suboptimal solutions.

Abstract

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.