# Neural Lyapunov Differentiable Predictive Control

arXiv: https://arxiv.org/abs/2205.10728 · HTML: https://mlsanity.com/paper/2205.10728/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 45 references that are in the map.
- First posted on arXiv 22 May 2022.

## Builds on (most cited first, 25 of 25)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [Differentiable MPC for End-to-end Planning and Control](https://mlsanity.com/paper/1810.13400/) (2018)
- [Neural Lyapunov Control](https://mlsanity.com/paper/2005.00611/) (2020)
- [Learning Stable Deep Dynamics Models](https://mlsanity.com/paper/2001.06116/) (2020)
- [Safety Verification and Robustness Analysis of Neural Networks via Quadratic Constraints and Semidefinite Programming](https://mlsanity.com/paper/1903.01287/) (2019)
- [Optimal Control Via Neural Networks: A Convex Approach](https://mlsanity.com/paper/1805.11835/) (2018)
- [Safe Reinforcement Learning Using Robust MPC](https://mlsanity.com/paper/1906.04005/) (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)
- [Learning Deep Control Policies for Autonomous Aerial Vehicles with MPC-Guided Policy Search](https://mlsanity.com/paper/1509.06791/) (2015)
- [Enforcing robust control guarantees within neural network policies](https://mlsanity.com/paper/2011.08105/) (2020)
- [Large Scale Model Predictive Control with Neural Networks and Primal Active Sets](https://mlsanity.com/paper/1910.10835/) (2019)
- [Infinite-Horizon Differentiable Model Predictive Control](https://mlsanity.com/paper/2001.02244/) (2020)
- [Adaptive MPC for Iterative Tasks](https://mlsanity.com/paper/1804.09831/) (2018)
- [A Neural Network Architecture to Learn Explicit MPC Controllers from Data](https://mlsanity.com/paper/1911.10789/) (2019)
- [MPC-Inspired Neural Network Policies for Sequential Decision Making](https://mlsanity.com/paper/1802.05803/) (2018)
- [Probabilistic performance validation of deep learning-based robust NMPC controllers](https://mlsanity.com/paper/1910.13906/) (2019)
- [Deep Learning Explicit Differentiable Predictive Control Laws for Buildings](https://mlsanity.com/paper/2107.11843/) (2021)
- [Learning Constrained Adaptive Differentiable Predictive Control Policies With Guarantees](https://mlsanity.com/paper/2004.11184/) (2020)
- [Neural Lyapunov Model Predictive Control: Learning Safe Global Controllers from Sub-optimal Examples](https://mlsanity.com/paper/2002.10451/) (2020)
- [Learning Stochastic Parametric Differentiable Predictive Control Policies](https://mlsanity.com/paper/2203.01447/) (2022)
- [Neural Identification for Control](https://mlsanity.com/paper/2009.11782/) (2020)
- [Practical Comparison of Optimization Algorithms for Learning-Based MPC with Linear Models](https://mlsanity.com/paper/1404.2843/) (2014)

## Built on by (most cited first, 7 of 7)

- [Physics-Informed Machine Learning for Modeling and Control of Dynamical Systems](https://mlsanity.com/paper/2306.13867/) (2023)
- [Differentiable Safe Controller Design through Control Barrier Functions](https://mlsanity.com/paper/2209.10034/) (2022)
- [A view on learning robust goal-conditioned value functions: Interplay between RL and MPC](https://mlsanity.com/paper/2502.06996/) (2025)
- [(Un)supervised Learning of Maximal Lyapunov Functions](https://mlsanity.com/paper/2408.17246/) (2024)
- [Lyapunov Neural ODE State-Feedback Control Policies](https://mlsanity.com/paper/2409.00393/) (2024)
- [CIKAN: Constraint Informed Kolmogorov-Arnold Networks for Autonomous Spacecraft Rendezvous using Time Shift Governor](https://mlsanity.com/paper/2412.03710/) (2024)
- [partialCBDs: Differentiable Causal Block Diagrams](https://mlsanity.com/paper/2602.07581/) (2026)

## Abstract (arXiv)

We present a learning-based predictive control methodology using the differentiable programming framework with probabilistic Lyapunov-based stability guarantees. The neural Lyapunov differentiable predictive control (NLDPC) learns the policy by constructing a computational graph encompassing the system dynamics, state and input constraints, and the necessary Lyapunov certification constraints, and thereafter using the automatic differentiation to update the neural policy parameters. In conjunction, our approach jointly learns a Lyapunov function that certifies the regions of state-space with stable dynamics. We also provide a sampling-based statistical guarantee for the training of NLDPC from the distribution of initial conditions. Our offline training approach provides a computationally efficient and scalable alternative to classical explicit model predictive control solutions. We substantiate the advantages of the proposed approach with simulations to stabilize the double integrator model and on an example of controlling an aircraft model.