Bayesian Forecasting with Deep Generative Disturbance Models in Stochastic MPC for Building Energy Systems

Predictive control strongly depends on the quality of disturbance predictions. While recent disturbance modeling efforts have adopted a probabilistic perspective to protect against unreliable deterministic predictions, such probabilistic models are often applicable only in data-rich settings or involve making simplifying assumptions on the underlying distributions. Generative models, such as conditional variational autoencoders (CVAEs), provide an expressive and automated approach for learning distributions from data. By sampling the learned latent space, one can generate unseen disturbance realizations. In this paper, we develop methods to leverage these generative models for the design of economic stochastic model predictive control (SMPC) that utilizes disturbance signals generated by a CVAE for online adaptation. Scenarios generated by the CVAE can be transformed to conditional probabilities on learned latent vectors, wherein the conditioning is with respect to factors that affect the disturbance signal shape itself (e.g., effect of workday/weekend on internal heat loads) along with the observed data (i.e., how likely the latent is, based on the observed data). We can consequently generate the most relevant disturbance signals for use in a scenario tree-based SMPC approach to reduce conservativeness of the control policy while satisfying constraints.