End-to-End Differentiable Predictive Control with Probabilistic Constraint-Satisfaction Guarantees for Building Demand Response

Abstract

Building Demand Response (DR) benefits from Model Predictive Control (MPC) because thermal flexibility can be optimized over a future horizon while enforcing operational constraints, but the repeated online optimization required by MPC motivates Differentiable Predictive Control (DPC) as a computationally efficient explicit-policy alternative. Conventional DPC, however, separates model identification from policy optimization and remains sensitive to plant-model mismatch. This paper proposes an End-to-End DPC (E2E-DPC) framework that jointly optimizes the learned dynamics model and control policy using prediction, constraint, and economic objectives. Stage-wise conformal prediction (CP) calibrates recursive prediction errors to construct horizon-dependent tightened state constraints, while independent Hoeffding certification provides a high-confidence lower bound on plant-level satisfaction of the original state and input constraints under receding-horizon deployment. The framework is evaluated in a high-fidelity residential building simulation using EnergyPlus through the Energym interface and compared with online MPC and conventional DPC. Constraint tightening eliminates thermal violations for both DPC variants in the stress test and reduces violations by 99.4 percent for online MPC. Compared with conventional DPC, E2E-DPC reduces the mean constraint-tightening margin at the first prediction stage by 31.0 percent and increases the median certified plant-level lower bound from 0 to 0.814. The results further reveal a trade-off between stronger certification of plant-level constraint satisfaction and the ability to maintain nonempty tightened state sets as the prediction horizon increases, with stronger multi-step identification mitigating this trade-off.

18 pages, 5 figures. Substantially revised version: replaced the previous deterministic tube-based constraint-tightening formulation with stage-wise conformal prediction and independent Hoeffding certification; expanded theoretical analysis, experiments, and comparisons