Model Predictive Control with Recursive Multi-step Input Convex Lipschitz Neural Networks: an Application to Smart Buildings

Model Predictive Control (MPC) is an optimal control technique that employs a dynamic model of the controlled process and an optimization algorithm to determine the control strategy. Nevertheless, the cost and effort required to create and maintain dynamical models are often high, and solving the resulting optimal control problem can be computationally complex. In recent years, data-driven modeling has become an attractive alternative to approximate the behavior of dynamical systems, with the aim of alleviating these issues. However, using such models for model-based control can be challenging due to their typically nonlinear and nonconvex nature. To address these issues, we propose a recursive multi-step learning-based dynamical modeling framework to capture the temporal behavior of dynamic systems. We take advantage of Input Convex Lipschitz Neural Networks, which are explicitly designed to be convex and continuous with respect to their in-puts. We further show that these mathematical proprieties hold in a multi-step dynamical modeling framework. The proposed approach is evaluated in a real-life MPC experiment conducted in a smart building in the Samso Marina, Denmark. We show that the proposed approach keeps the internal temperature within comfort constraints while minimizing heating/cooling energy consumption.