# Probabilistic Guarantees for Nonlinear Safety-Critical Optimal Control

arXiv: https://arxiv.org/abs/2303.06258 · HTML: https://mlsanity.com/paper/2303.06258/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Mar 2023.

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

- [Verifiable Learned Behaviors via Motion Primitive Composition: Applications to Scooping of Granular Media](https://mlsanity.com/paper/2309.14894/) (2023)

## Abstract (arXiv)

Leveraging recent developments in black-box risk-aware verification, we provide three algorithms that generate probabilistic guarantees on (1) optimality of solutions, (2) recursive feasibility, and (3) maximum controller runtimes for general nonlinear safety-critical finite-time optimal controllers. These methods forego the usual (perhaps) restrictive assumptions required for typical theoretical guarantees, e.g. terminal set calculation for recursive feasibility in Nonlinear Model Predictive Control, or convexification of optimal controllers to ensure optimality. Furthermore, we show that these methods can directly be applied to hardware systems to generate controller guarantees on their respective systems.