# Neural Lyapunov Model Predictive Control: Learning Safe Global Controllers from Sub-optimal Examples

arXiv: https://arxiv.org/abs/2002.10451 · HTML: https://mlsanity.com/paper/2002.10451/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Feb 2020.

## Built on by (most cited first, 5 of 5)

- [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)
- [Model Predictive Control and Reinforcement Learning: A Unified Framework Based on Dynamic Programming](https://mlsanity.com/paper/2406.00592/) (2024)
- [Certifying Stability of Reinforcement Learning Policies using Generalized Lyapunov Functions](https://mlsanity.com/paper/2505.10947/) (2025)
- [KEEC: Koopman Embedded Equivariant Control](https://mlsanity.com/paper/2312.01544/) (2023)

## Abstract (arXiv)

With a growing interest in data-driven control techniques, Model Predictive Control (MPC) provides an opportunity to exploit the surplus of data reliably, particularly while taking safety and stability into account. In many real-world and industrial applications, it is typical to have an existing control strategy, for instance, execution from a human operator. The objective of this work is to improve upon this unknown, safe but suboptimal policy by learning a new controller that retains safety and stability. Learning how to be safe is achieved directly from data and from a knowledge of the system constraints. The proposed algorithm alternatively learns the terminal cost and updates the MPC parameters according to a stability metric. The terminal cost is constructed as a Lyapunov function neural network with the aim of recovering or extending the stable region of the initial demonstrator using a short prediction horizon. Theorems that characterize the stability and performance of the learned MPC in the bearing of model uncertainties and sub-optimality due to function approximation are presented. The efficacy of the proposed algorithm is demonstrated on non-linear continuous control tasks with soft constraints. The proposed approach can improve upon the initial demonstrator also in practice and achieve better stability than popular reinforcement learning baselines.