# Efficient computation of Lipschitz constants for MPC with symmetries

arXiv: https://arxiv.org/abs/2311.04580 · HTML: https://mlsanity.com/paper/2311.04580/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Nov 2023.

## Built on by (most cited first, 1 of 1)

- [Imitation Learning of MPC with Neural Networks: Error Guarantees and Sparsification](https://mlsanity.com/paper/2501.03671/) (2025)

## Abstract (arXiv)

Lipschitz constants for linear MPC are useful for certifying inherent robustness against unmodeled disturbances or robustness for neural network-based approximations of the control law. In both cases, knowing the minimum Lipschitz constant leads to less conservative certifications. Computing this minimum Lipschitz constant is trivial given the explicit MPC. However, the computation of the explicit MPC may be intractable for complex systems. The paper discusses a method for efficiently computing the minimum Lipschitz constant without using the explicit control law. The proposed method simplifies a recently presented mixed-integer linear program (MILP) that computes the minimum Lipschitz constant. The simplification is obtained by exploiting saturation and symmetries of the control law and irrelevant constraints of the optimal control problem.