Beyond Model Accuracy: Learning Control-Oriented State-Space Models for Building MPC

Abstract

MPC offers a systematic way to reduce energy use in building climate control while respecting comfort and actuator constraints, but its practical performance depends on prediction models that remain reliable inside a receding-horizon optimization problem. This thesis develops TNGDI, a physics-guided differentiable identification method for compact LTI state-space models of multi-zone building thermal dynamics. Most importantly, the method parameterizes a continuous-time model with topology masks based on building layout, a Metzler state matrix to encode thermal RC network dynamics, and nonnegative heat-input gains. The approach is evaluated on a linear five-zone simulation plant and compared with an N4SID subspace-identification baseline using prediction error, heat-response plausibility, and closed-loop performance in offset-free EMPC. The N4SID baseline achieves a slightly lower test RMSE than the proposed model, 0.39 °C compared to 0.43 °C, but it also produces physically implausible heat-input mappings from one radiator to the zones. The proposed model preserves nonnegative heat responses over the evaluated horizon. In a seven-day offset-free EMPC comparison, the TNGDI-based controller uses 25% less heating energy and incurs 8% less comfort violation than the N4SID-based controller. These results support the thesis claim that open-loop accuracy alone is insufficient for control-oriented model selection: a model with larger prediction error can be more suitable for MPC when its actuator-response sign is physically plausible. The validation remains limited to an idealized case study with a linear plant, noiseless measurements, and perfect disturbance forecasts.