[Paper Review] Input Convex Neural Networks for Building MPC

Felix Bünning, Adrian Schalbetter+4 more|arXiv (Cornell University)|Nov 26, 2020

Advanced Control Systems Optimization12 references33 citations

TL;DR

The paper adapts Input Convex Neural Networks (ICNNs) to enable multi-step ahead predictions within Model Predictive Control (MPC) for building energy management, and validates them in numerical and real-world experiments.

ABSTRACT

Model Predictive Control in buildings can significantly reduce their energy consumption. The cost and effort necessary for creating and maintaining first principle models for buildings make data-driven modelling an attractive alternative in this domain. In MPC the models form the basis for an optimization problem whose solution provides the control signals to be applied to the system. The fact that this optimization problem has to be solved repeatedly in real-time implies restrictions on the learning architectures that can be used. Here, we adapt Input Convex Neural Networks that are generally only convex for one-step predictions, for use in building MPC. We introduce additional constraints to their structure and weights to achieve a convex input-output relationship for multistep ahead predictions. We assess the consequences of the additional constraints for the model accuracy and test the models in a real-life MPC experiment in an apartment in Switzerland. In two five-day cooling experiments, MPC with Input Convex Neural Networks is able to keep room temperatures within comfort constraints while minimizing cooling energy consumption.

Motivation & Objective

• Motivate data-driven modeling for building MPC to reduce energy use without expensive first-principles models.
• Extend ICNN architectures to achieve convex input-output relations for multi-step ahead predictions.
• Embed ICNN-based dynamics in (quasi-)convex MPC and address lower state constraints via slack variables.
• Evaluate prediction accuracy versus prior ICNN formulations and demonstrate real-life MPC performance in an occupied apartment.

Proposed method

• Use Fully ICNN (FICNN) and Partially ICNN (PICNN) architectures with additional constraints and activation functions to ensure convexity for multi-step predictions.
• Prove that compositions of convex, non-decreasing activations with non-negative weight matrices preserve convexity in multi-step forecasts (Propositions 1 and 2).
• Embed the ICNN dynamics into (quasi-)convex MPC formulations with convex or quasi-convex cost functions and soft state constraints via slack variables.
• Compare prediction accuracy against Amos et al. (2017) networks using real apartment data with cross-validated folds.
• Conduct two real experiments in a two-bedroom UMAR apartment to assess MPC performance with FICNN and PICNN in maintaining comfort while minimizing cooling energy.

Experimental results

Research questions

• RQ1 Can ICNN-based models be made convex for multi-step ahead predictions suitable for MPC in buildings?
• RQ2 How do FICNN and PICNN perform in terms of prediction accuracy compared to prior ICNN formulations for building temperature dynamics?
• RQ3 Can ICNN-based dynamics be embedded in (quasi-)convex MPC with soft state constraints while ensuring feasible real-time optimization?
• RQ4 What is the practical performance of ICNN-driven MPC in real apartment experiments for cooling energy savings and comfort maintenance?

Key findings

• Multi-step convexity can be achieved for FICNN and PICNN through architectural constraints and ReLU-based activations (Propositions 1 and 2).
• In numerical tests, Amos networks show lower MSE for 1-hour and 6-hour predictions than the proposed ICNN variants, indicating a trade-off between convexity constraints and flexibility.
• In two real experiments, MPC with ICNNs kept room temperatures within time-varying comfort constraints while reducing cooling energy use.
• PICNN tended to avoid overcooling and matched upper comfort limits at key times, while FICNN sometimes cooled more than necessary.