# Deep Learning Alternative to Explicit Model Predictive Control for Unknown Nonlinear Systems

arXiv: https://arxiv.org/abs/2011.03699 · HTML: https://mlsanity.com/paper/2011.03699/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Nov 2020.

## Built on by (most cited first, 22 of 22)

- [Physics-Informed Machine Learning for Modeling and Control of Dynamical Systems](https://mlsanity.com/paper/2306.13867/) (2023)
- [Closing the Planning-Learning Loop with Application to Autonomous Driving](https://mlsanity.com/paper/2101.03834/) (2021)
- [Real-Time Decision-Making for Digital Twin in Additive Manufacturing with Model Predictive Control using Time-Series Deep Neural Networks](https://mlsanity.com/paper/2501.07601/) (2025)
- [Diffusion-Based Approximate MPC: Fast and Consistent Imitation of Multi-Modal Action Distributions](https://mlsanity.com/paper/2504.04603/) (2025)
- [ZipMPC: Compressed Context-Dependent MPC Cost via Imitation Learning](https://mlsanity.com/paper/2507.13088/) (2025)
- [YANNs: Y-wise Affine Neural Networks for Exact and Efficient Representations of Piecewise Linear Functions](https://mlsanity.com/paper/2505.07054/) (2025)
- [Plug-and-Play Benchmarking of Reinforcement Learning Algorithms for Large-Scale Flow Control](https://mlsanity.com/paper/2601.15015/) (2026)
- [A Physics-informed Machine Learning-based Control Method for Nonlinear Dynamic Systems with Highly Noisy Measurements](https://mlsanity.com/paper/2311.07613/) (2023)
- [Three Pathways to Neurosymbolic Reinforcement Learning with Interpretable Model and Policy Networks](https://mlsanity.com/paper/2402.05307/) (2024)
- [Differentiable Predictive Control for Large-Scale Urban Road Networks](https://mlsanity.com/paper/2406.10433/) (2024)
- [Error whitening: Why Gauss-Newton outperforms Newton](https://mlsanity.com/paper/2605.11316/) (2026)
- [Inverse Boundary Value and Optimal Control Problems on Graphs: A Neural and Numerical Synthesis](https://mlsanity.com/paper/2206.02911/) (2022)
- [Neural Control System for Continuous Glucose Monitoring and Maintenance](https://mlsanity.com/paper/2402.13852/) (2024)
- [Lyapunov Neural ODE State-Feedback Control Policies](https://mlsanity.com/paper/2409.00393/) (2024)
- [Learning-Based Approximate Nonlinear Model Predictive Control Motion Cueing](https://mlsanity.com/paper/2504.00469/) (2025)
- [First Contact: Data-driven Friction-Stir Process Control](https://mlsanity.com/paper/2507.03177/) (2025)
- [Comparative Field Deployment of Reinforcement Learning and Model Predictive Control for Residential HVAC](https://mlsanity.com/paper/2510.01475/) (2025)
- [Zero-Shot Function Encoder-Based Differentiable Predictive Control](https://mlsanity.com/paper/2511.05757/) (2025)
- [Why Goal-Conditioned Reinforcement Learning Works: Relation to Dual Control](https://mlsanity.com/paper/2512.06471/) (2025)
- [partialCBDs: Differentiable Causal Block Diagrams](https://mlsanity.com/paper/2602.07581/) (2026)
- [Topological Feasibility Guarantees for Differentiable Predictive Control](https://mlsanity.com/paper/2608.10332/) (2026)
- [SD-DPC: Sparse Dictionary Differentiable Predictive Control](https://mlsanity.com/paper/2610.02466/) (2026)

## Abstract (arXiv)

We present differentiable predictive control (DPC) as a deep learning-based alternative to the explicit model predictive control (MPC) for unknown nonlinear systems. In the DPC framework, a neural state-space model is learned from time-series measurements of the system dynamics. The neural control policy is then optimized via stochastic gradient descent approach by differentiating the MPC loss function through the closed-loop system dynamics model. The proposed DPC method learns model-based control policies with state and input constraints, while supporting time-varying references and constraints. In embedded implementation using a Raspberry-Pi platform, we experimentally demonstrate that it is possible to train constrained control policies purely based on the measurements of the unknown nonlinear system. We compare the control performance of the DPC method against explicit MPC and report efficiency gains in online computational demands, memory requirements, policy complexity, and construction time. In particular, we show that our method scales linearly compared to exponential scalability of the explicit MPC solved via multiparametric programming.