# Real-Time Adaptive Safety-Critical Control with Gaussian Processes in High-Order Uncertain Models

arXiv: https://arxiv.org/abs/2402.18946 · HTML: https://mlsanity.com/paper/2402.18946/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 34 references that are in the map.
- First posted on arXiv 29 Feb 2024.

## Builds on (most cited first, 21 of 21)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Pyro: Deep Universal Probabilistic Programming](https://mlsanity.com/paper/1810.09538/) (2018)
- [Control Barrier Functions: Theory and Applications](https://mlsanity.com/paper/1903.11199/) (2019)
- [Meta-Learning Priors for Efficient Online Bayesian Regression](https://mlsanity.com/paper/1807.08912/) (2018)
- [Streaming Sparse Gaussian Process Approximations](https://mlsanity.com/paper/1705.07131/) (2017)
- [Safe Learning of Quadrotor Dynamics Using Barrier Certificates](https://mlsanity.com/paper/1710.05472/) (2017)
- [Guaranteeing Safety of Learned Perception Modules via Measurement-Robust Control Barrier Functions](https://mlsanity.com/paper/2010.16001/) (2020)
- [Robustness of Control Barrier Functions for Safety Critical Control](https://mlsanity.com/paper/1612.01554/) (2016)
- [Adaptive Safety with Control Barrier Functions](https://mlsanity.com/paper/1910.00555/) (2019)
- [Control Barrier Functions for Unknown Nonlinear Systems using Gaussian Processes](https://mlsanity.com/paper/2010.05818/) (2020)
- [Bayesian Learning-Based Adaptive Control for Safety Critical Systems](https://mlsanity.com/paper/1910.02325/) (2019)
- [Meta-Reinforcement Learning via Language Instructions](https://mlsanity.com/paper/2209.04924/) (2022)
- [Control Barriers in Bayesian Learning of System Dynamics](https://mlsanity.com/paper/2012.14964/) (2020)
- [Pointwise Feasibility of Gaussian Process-based Safety-Critical Control under Model Uncertainty](https://mlsanity.com/paper/2106.07108/) (2021)
- [Gaussian Process-based Min-norm Stabilizing Controller for Control-Affine Systems with Uncertain Input Effects and Dynamics](https://mlsanity.com/paper/2011.07183/) (2020)
- [Meta-Reinforcement Learning in Broad and Non-Parametric Environments](https://mlsanity.com/paper/2108.03718/) (2021)
- [Robust Control Barrier Functions with Sector-Bounded Uncertainties](https://mlsanity.com/paper/2109.02537/) (2021)
- [Learning from Symmetry: Meta-Reinforcement Learning with Symmetrical Behaviors and Language Instructions](https://mlsanity.com/paper/2209.10656/) (2022)
- [Complex Robotic Manipulation via Graph-Based Hindsight Goal Generation](https://mlsanity.com/paper/2007.13486/) (2020)
- [Adaptive Sparse Gaussian Process](https://mlsanity.com/paper/2302.10325/) (2023)
- [Stable Model-based Control with Gaussian Process Regression for Robot Manipulators](https://mlsanity.com/paper/1811.06655/) (2018)

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

- [Inference-stage Adaptation-projection Strategy Adapts Diffusion Policy to Cross-manipulators Scenarios](https://mlsanity.com/paper/2509.11621/) (2025)

## Abstract (arXiv)

This paper presents an adaptive online learning framework for systems with uncertain parameters to ensure safety-critical control in non-stationary environments. Our approach consists of two phases. The initial phase is centered on a novel sparse Gaussian process (GP) framework. We first integrate a forgetting factor to refine a variational sparse GP algorithm, thus enhancing its adaptability. Subsequently, the hyperparameters of the Gaussian model are trained with a specially compound kernel, and the Gaussian model's online inferential capability and computational efficiency are strengthened by updating a solitary inducing point derived from new samples, in conjunction with the learned hyperparameters. In the second phase, we propose a safety filter based on high-order control barrier functions (HOCBFs), synergized with the previously trained learning model. By leveraging the compound kernel from the first phase, we effectively address the inherent limitations of GPs in handling high-dimensional problems for real-time applications. The derived controller ensures a rigorous lower bound on the probability of satisfying the safety specification. Finally, the efficacy of our proposed algorithm is demonstrated through real-time obstacle avoidance experiments executed using both a simulation platform and a real-world 7-DOF robot.