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Model Predictive Control and Moving Horizon Estimation using Statistically Weighted Data-Based Ensemble Models

Laura Boca de Giuli, Samuel Mallick, Alessio La Bella, Azita Dabiri, Bart De Schutter, Riccardo Scattolini

TL;DR

This work tackles MPC for systems operating under multiple conditions by using an ensemble of data-based models and dynamically weighting their predictions. A Mahalanobis distance-based weighting rule assigns ensemble weights as a function of the current input, allowing weights to vary across the prediction horizon and to favor models trained on inputs closest to the current regime. An accompanying MHE-based observer estimates each ensemble model's state with constraints, providing accurate initialization for MPC. Validation on a district heating benchmark shows that the horizon-optimized Mahalanobis-based weighting (MD-2) yields the best economic performance and constraint satisfaction, while the MHE observer markedly improves state and output accuracy.

Abstract

This paper presents a model predictive control (MPC) framework leveraging an ensemble of data-based models to optimally control complex systems under multiple operating conditions. A novel combination rule for ensemble models is proposed, based on the statistical Mahalanobis distance, enabling the ensemble weights to suitably vary across the prediction window based on the system input. In addition, a novel state observer for ensemble models is developed using moving horizon estimation (MHE). The effectiveness of the proposed methodology is demonstrated on a benchmark energy system operating under multiple conditions.

Model Predictive Control and Moving Horizon Estimation using Statistically Weighted Data-Based Ensemble Models

TL;DR

This work tackles MPC for systems operating under multiple conditions by using an ensemble of data-based models and dynamically weighting their predictions. A Mahalanobis distance-based weighting rule assigns ensemble weights as a function of the current input, allowing weights to vary across the prediction horizon and to favor models trained on inputs closest to the current regime. An accompanying MHE-based observer estimates each ensemble model's state with constraints, providing accurate initialization for MPC. Validation on a district heating benchmark shows that the horizon-optimized Mahalanobis-based weighting (MD-2) yields the best economic performance and constraint satisfaction, while the MHE observer markedly improves state and output accuracy.

Abstract

This paper presents a model predictive control (MPC) framework leveraging an ensemble of data-based models to optimally control complex systems under multiple operating conditions. A novel combination rule for ensemble models is proposed, based on the statistical Mahalanobis distance, enabling the ensemble weights to suitably vary across the prediction window based on the system input. In addition, a novel state observer for ensemble models is developed using moving horizon estimation (MHE). The effectiveness of the proposed methodology is demonstrated on a benchmark energy system operating under multiple conditions.

Paper Structure

This paper contains 7 sections, 16 equations, 4 figures, 1 table.

Table of Contents

  1. INTRODUCTION
  2. Notation and preliminaries
  3. Problem statement
  4. MPC with Mahalanobis distance-based ensemble model
  5. MHE-based observer for ensemble models
  6. Numerical Results
  7. Conclusions

Figures (4)

  • Figure 1: Schematic representation of the AROMA DHS and its variables.
  • Figure 2: a) Five thermal demand profiles. b) Electricity price trend. c) Temperature lower bound profiles: dashed for $T_0^\text{r}$, solid line for $T_j^\text{c}$.
  • Figure 3: First day of simulation showing the five load supply temperatures $T_j^\text{s}$ along with the corresponding constraints (black dashed lines) under the different control strategies.
  • Figure 4: Output error $e^{[i]}$ for model in open-loop (solid blue) and with MHE-based state estimation (dashed red).

Theorems & Definitions (1)

  • Definition II.1