# Controlled Invariant Sets for Gaussian Process State Space Models

arXiv: https://arxiv.org/abs/2407.11256 · HTML: https://mlsanity.com/paper/2407.11256/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jul 2024.

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

- [Data-Driven Synthesis of Probabilistic Controlled Invariant Sets for Linear MDPs](https://mlsanity.com/paper/2604.02727/) (2026)

## Abstract (arXiv)

We compute probabilistic controlled invariant sets for nonlinear systems using Gaussian process state space models, which are data-driven models that account for unmodeled and unknown nonlinear dynamics. We propose a semidefinite programming scheme for designing state-feedback controllers that maximize the probability of the trajectories staying within a probabilistic controlled invariant set while satisfying input constraints. The results are validated on a quadrotor, both in simulation and on a physical platform.