# Safe and High-Performance Learning of Model Predicitve Control using Kernel-Based Interpolation

arXiv: https://arxiv.org/abs/2410.06771 · HTML: https://mlsanity.com/paper/2410.06771/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 38 references that are in the map.
- First posted on arXiv 9 Oct 2024.

## Builds on (most cited first, 10 of 10)

- [An Algorithmic Perspective on Imitation Learning](https://mlsanity.com/paper/1811.06711/) (2018)
- [Gaussian Processes and Kernel Methods: A Review on Connections and Equivalences](https://mlsanity.com/paper/1807.02582/) (2018)
- [Just Interpolate: Kernel "Ridgeless" Regression Can Generalize](https://mlsanity.com/paper/1808.00387/) (2018)
- [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)
- [Open- and Closed-Loop Neural Network Verification using Polynomial Zonotopes](https://mlsanity.com/paper/2207.02715/) (2022)
- [Automatic nonlinear MPC approximation with closed-loop guarantees](https://mlsanity.com/paper/2312.10199/) (2023)
- [Probabilistic performance validation of deep learning-based robust NMPC controllers](https://mlsanity.com/paper/1910.13906/) (2019)
- [Learning Soft Constrained MPC Value Functions: Efficient MPC Design and Implementation providing Stability and Safety Guarantees](https://mlsanity.com/paper/2401.07780/) (2024)
- [NMPC in Active Subspaces: Dimensionality Reduction with Recursive Feasibility Guarantees](https://mlsanity.com/paper/2209.10915/) (2022)

## Abstract (arXiv)

We present a method that allows efficient and safe approximation of model predictive controllers using kernel interpolation. Since the computational complexity of the approximating function scales linearly with the number of data points, we propose to use a scoring function which chooses the most promising data. To further reduce the complexity of the approximation, we restrict our considerations to the set of closed-loop reachable states. That is, the approximating function only has to be accurate within this set. This makes our method especially suited for systems, where the set of initial conditions is small. In order to guarantee safety and high performance of the designed approximated controller, we use reachability analysis based on Monte Carlo methods.