# Learning Constrained Adaptive Differentiable Predictive Control Policies With Guarantees

arXiv: https://arxiv.org/abs/2004.11184 · HTML: https://mlsanity.com/paper/2004.11184/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Apr 2020.

## Built on by (most cited first, 10 of 10)

- [Neural Ordinary Differential Equations for Nonlinear System Identification](https://mlsanity.com/paper/2203.00120/) (2022)
- [Learning Differentiable Safety-Critical Control using Control Barrier Functions for Generalization to Novel Environments](https://mlsanity.com/paper/2201.01347/) (2022)
- [Approximate non-linear model predictive control with safety-augmented neural networks](https://mlsanity.com/paper/2304.09575/) (2023)
- [Differentiable Safe Controller Design through Control Barrier Functions](https://mlsanity.com/paper/2209.10034/) (2022)
- [Neural Lyapunov Differentiable Predictive Control](https://mlsanity.com/paper/2205.10728/) (2022)
- [No More Pesky Hyperparameters: Offline Hyperparameter Tuning for RL](https://mlsanity.com/paper/2205.08716/) (2022)
- [Differentiable Predictive Control with Safety Guarantees: A Control Barrier Function Approach](https://mlsanity.com/paper/2208.02319/) (2022)
- [Learning Stochastic Parametric Differentiable Predictive Control Policies](https://mlsanity.com/paper/2203.01447/) (2022)
- [Neural ODEs as Feedback Policies for Nonlinear Optimal Control](https://mlsanity.com/paper/2210.11245/) (2022)
- [Three Pathways to Neurosymbolic Reinforcement Learning with Interpretable Model and Policy Networks](https://mlsanity.com/paper/2402.05307/) (2024)

## Abstract (arXiv)

We present differentiable predictive control (DPC), a method for learning constrained neural control policies for linear systems with probabilistic performance guarantees. We employ automatic differentiation to obtain direct policy gradients by backpropagating the model predictive control (MPC) loss function and constraints penalties through a differentiable closed-loop system dynamics model. We demonstrate that the proposed method can learn parametric constrained control policies to stabilize systems with unstable dynamics, track time-varying references, and satisfy nonlinear state and input constraints. In contrast with imitation learning-based approaches, our method does not depend on a supervisory controller. Most importantly, we demonstrate that, without losing performance, our method is scalable and computationally more efficient than implicit, explicit, and approximate MPC. Under review at IEEE Transactions on Automatic Control.