# Deep Learning Explicit Differentiable Predictive Control Laws for Buildings

arXiv: https://arxiv.org/abs/2107.11843 · HTML: https://mlsanity.com/paper/2107.11843/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 36 references that are in the map.
- First posted on arXiv 25 Jul 2021.

## Builds on (most cited first, 11 of 11)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Differentiable MPC for End-to-end Planning and Control](https://mlsanity.com/paper/1810.13400/) (2018)
- [Differentiating Through a Cone Program](https://mlsanity.com/paper/1904.09043/) (2019)
- [Efficient representation and approximation of model predictive control laws via deep learning](https://mlsanity.com/paper/1806.10644/) (2018)
- [Learning an Approximate Model Predictive Controller with Guarantees](https://mlsanity.com/paper/1806.04167/) (2018)
- [Imposing Hard Constraints on Deep Networks: Promises and Limitations](https://mlsanity.com/paper/1706.02025/) (2017)
- [Physics-constrained Deep Learning of Multi-zone Building Thermal Dynamics](https://mlsanity.com/paper/2011.05987/) (2020)
- [Infinite-Horizon Differentiable Model Predictive Control](https://mlsanity.com/paper/2001.02244/) (2020)
- [Safe and Near-Optimal Policy Learning for Model Predictive Control using Primal-Dual Neural Networks](https://mlsanity.com/paper/1906.08257/) (2019)
- [Constrained Neural Ordinary Differential Equations with Stability Guarantees](https://mlsanity.com/paper/2004.10883/) (2020)

## Built on by (most cited first, 11 of 11)

- [Physics-Informed Machine Learning for Modeling and Control of Dynamical Systems](https://mlsanity.com/paper/2306.13867/) (2023)
- [Neural Lyapunov Differentiable Predictive Control](https://mlsanity.com/paper/2205.10728/) (2022)
- [Differentiable Predictive Control with Safety Guarantees: A Control Barrier Function Approach](https://mlsanity.com/paper/2208.02319/) (2022)
- [Imitation Learning from Nonlinear MPC via the Exact Q-Loss and its Gauss-Newton Approximation](https://mlsanity.com/paper/2304.01782/) (2023)
- [Learning Stochastic Parametric Differentiable Predictive Control Policies](https://mlsanity.com/paper/2203.01447/) (2022)
- [Stable Linear Subspace Identification: A Machine Learning Approach](https://mlsanity.com/paper/2311.03197/) (2023)
- [Differentiable Predictive Control for Large-Scale Urban Road Networks](https://mlsanity.com/paper/2406.10433/) (2024)
- [Data-Driven Adaptive PID Control Based on Physics-Informed Neural Networks](https://mlsanity.com/paper/2510.04591/) (2025)
- [Neuro-physical dynamic load modeling using differentiable parametric optimization](https://mlsanity.com/paper/2203.10582/) (2022)
- [Domain-aware Control-oriented Neural Models for Autonomous Underwater Vehicles](https://mlsanity.com/paper/2208.07333/) (2022)
- [Safety Reinforced Model Predictive Control (SRMPC): Improving MPC with Reinforcement Learning for Motion Planning in Autonomous Driving](https://mlsanity.com/paper/2512.03774/) (2025)

## Abstract (arXiv)

We present a differentiable predictive control (DPC) methodology for learning constrained control laws for unknown nonlinear systems. DPC poses an approximate solution to multiparametric programming problems emerging from explicit nonlinear model predictive control (MPC). Contrary to approximate MPC, DPC does not require supervision by an expert controller. Instead, a system dynamics model is learned from the observed system's dynamics, and the neural control law is optimized offline by leveraging the differentiable closed-loop system model. The combination of a differentiable closed-loop system and penalty methods for constraint handling of system outputs and inputs allows us to optimize the control law's parameters directly by backpropagating economic MPC loss through the learned system model. The control performance of the proposed DPC method is demonstrated in simulation using learned model of multi-zone building thermal dynamics.