Model Predictive Control of Heating Systems via Koopman-Operator Bilinearization

Abstract

Hydronic heat emitters are widely used in buildings, but their control is challenging due to nonlinear dynamics, arising from both the heat transfer in each emitter and the hydraulic coupling among those that share a circulating pump. These nonlinearities are often simplified or neglected in the literature. In this paper, we use Koopman theory to make the resulting model more tractable for control. In particular, we propose an input reparameterization and construct an infinite-dimensional set of observables that yields an exact bilinear representation of the system in the chosen lifted space. We then show that truncating the infinite-dimensional representation leads to bounded approximation errors that decrease as the truncation order increases, as well as bounded trajectory deviations over a finite horizon. The resulting bilinear model is incorporated into a model predictive control (MPC) framework to provide thermal comfort in multi-zone buildings while reducing energy use. Using a numerical case study of a five-story building with 20 zones, we show that the proposed Koopman-based MPC achieves a realized performance cost close to that of nonlinear MPC with faster solve times, and outperforms MPC formulations based on time-invariant and time-varying linearizations.