Model Predictive Control (MPC) is a model-based technique widely and successfully used over the past years to improve control systems performance. A key factor prohibiting the widespread adoption of MPC for complex systems such as buildings is related to the difficulties (cost, time and effort) associated with the identification of a predictive model of a building. To overcome this problem, we introduce a novel idea for predictive control based on historical building data leveraging machine learning algorithms like regression trees and random forests. We call this approach Data-driven model Predictive Control (DPC), and we apply it to three different case studies to demonstrate its performance, scalability, and robustness. In the first case study we consider a benchmark MPC controller using a bilinear building model, then we apply DPC to a data-set simulated from such bilinear model and derive a controller based only on the data. Our results demonstrate that DPC can provide comparable performance with respect to MPC applied to a perfectly known mathematical model. In the second case study, we apply DPC to a 6 story 22 zone building model in EnergyPlus, for which model-based control is not economical and practical due to extreme complexity, and address a Demand Response problem. Our results demonstrate scalability and efficiency of DPC showing that DPC provides the desired power curtailment with an average error of 3%. In the third case study, we implement and test DPC on real data from an off-grid house located in L' Aquila, Italy. We compare the total amount of energy saved with respect to the classical bang-bang controller, showing that we can perform an energy saving up to 49.2%. Our results demonstrate the robustness of our method to uncertainties both in real data acquisition and weather forecast.

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Building physics-based models of complex physical systems like buildings and chemical plants is extremely cost and time prohibitive for applications such as real-time optimal control, production planning and supply chain logistics. Machine learning algorithms can reduce this cost and time complexity, and are, consequently, more scalable for large-scale physical systems. However, there are many practical challenges that must be addressed before employing machine learning for closed-loop control. This paper proposes the use of Gaussian Processes (GP) for learning control-oriented models: (1) We develop methods for the optimal experiment design (OED) of functional tests to learn models of a physical system, subject to stringent operational constraints and limited availability of the system. Using a Bayesian approach with GP, our methods seek to select the most informative data for optimally updating an existing model. (2) We also show that black-box GP models can be used for receding horizon optimal control with probabilistic guarantees on constraint satisfaction through chance constraints. (3) We further propose an online method for continuously improving the GP model in closed-loop with a real-time controller. Our methods are demonstrated and validated in a case study of building energy control and Demand Response.

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