# Probabilistic performance validation of deep learning-based robust NMPC controllers

arXiv: https://arxiv.org/abs/1910.13906 · HTML: https://mlsanity.com/paper/1910.13906/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Oct 2019.

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

- [Automatic nonlinear MPC approximation with closed-loop guarantees](https://mlsanity.com/paper/2312.10199/) (2023)
- [Approximate non-linear model predictive control with safety-augmented neural networks](https://mlsanity.com/paper/2304.09575/) (2023)
- [Neural Lyapunov Differentiable Predictive Control](https://mlsanity.com/paper/2205.10728/) (2022)
- [Learning Stochastic Parametric Differentiable Predictive Control Policies](https://mlsanity.com/paper/2203.01447/) (2022)
- [Self-Supervised Learning of Iterative Solvers for Constrained Optimization](https://mlsanity.com/paper/2409.08066/) (2024)
- [An Improved Data Augmentation Scheme for Model Predictive Control Policy Approximation](https://mlsanity.com/paper/2303.05607/) (2023)
- [Combining Federated Learning and Control: A Survey](https://mlsanity.com/paper/2407.11069/) (2024)
- [Neural Horizon Model Predictive Control -- Increasing Computational Efficiency with Neural Networks](https://mlsanity.com/paper/2408.09781/) (2024)
- [A Heuristic for Dynamic Output Predictive Control Design for Uncertain Nonlinear Systems](https://mlsanity.com/paper/2102.02268/) (2021)
- [Safe and High-Performance Learning of Model Predicitve Control using Kernel-Based Interpolation](https://mlsanity.com/paper/2410.06771/) (2024)
- [A Scalable Learned Iterative Solver for Nonlinear MPC via Temporal Decomposition](https://mlsanity.com/paper/2610.13480/) (2026)

## Abstract (arXiv)

Solving nonlinear model predictive control problems in real time is still an important challenge despite of recent advances in computing hardware, optimization algorithms and tailored implementations. This challenge is even greater when uncertainty is present due to disturbances, unknown parameters or measurement and estimation errors. To enable the application of advanced control schemes to fast systems and on low-cost embedded hardware, we propose to approximate a robust nonlinear model controller using deep learning and to verify its quality using probabilistic validation techniques. We propose a probabilistic validation technique based on finite families, combined with the idea of generalized maximum and constraint backoff to enable statistically valid conclusions related to general performance indicators. The potential of the proposed approach is demonstrated with simulation results of an uncertain nonlinear system.