Stochastic model predictive control with switched latent force models

Abstract

Switched latent force models (LFMs) are combinations of a first-principles physical model and a Gaussian process prior, where the driving force of the LFM may switch at certain time points. This allows to use expert knowledge to create an analytical state space model that describes large parts of the system behavior, while deviating parts are modeled using data-based methods. This paper proposes the combination of stochastic model predictive control and switched LFMs by reformulating the Gaussian process priors as linear state space models with additive white Gaussian noise. For this purpose, a stochastic optimization problem is formulated that can be solved by a deterministic approximation of the uncertainty propagation and the chance constraints. The switching points of the LFM introduce further uncertainty to the system that must be considered for the prediction of the state trajectories. Therefore, Gaussian mixture models are used to describe the probability density functions of the predicted states. The computation cost of the approach can be reduced by using a separate disturbance predictor, which allows to formulate the optimization problem of the model predictive controller independently of the internal disturbance states. The performance of the proposed method is illustrated for the control of a building energy system.