# Gaussian Process-based Min-norm Stabilizing Controller for Control-Affine Systems with Uncertain Input Effects and Dynamics

arXiv: https://arxiv.org/abs/2011.07183 · HTML: https://mlsanity.com/paper/2011.07183/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Nov 2020.

## Built on by (most cited first, 12 of 12)

- [Pointwise Feasibility of Gaussian Process-based Safety-Critical Control under Model Uncertainty](https://mlsanity.com/paper/2106.07108/) (2021)
- [Nonparametric Control Koopman Operators](https://mlsanity.com/paper/2405.07312/) (2024)
- [Efficient Motion Planning for Manipulators with Control Barrier Function-Induced Neural Controller](https://mlsanity.com/paper/2404.01184/) (2024)
- [Random Features Approximation for Control-Affine Systems](https://mlsanity.com/paper/2406.06514/) (2024)
- [Gaussian Control Barrier Functions : A Non-Parametric Paradigm to Safety](https://mlsanity.com/paper/2203.15474/) (2022)
- [Recursively Feasible Probabilistic Safe Online Learning with Control Barrier Functions](https://mlsanity.com/paper/2208.10733/) (2022)
- [Distributionally Robust Policy and Lyapunov-Certificate Learning](https://mlsanity.com/paper/2404.03017/) (2024)
- [Differentially Flat Learning-based Model Predictive Control Using a Stability, State, and Input Constraining Safety Filter](https://mlsanity.com/paper/2307.10541/) (2023)
- [Real-Time Adaptive Safety-Critical Control with Gaussian Processes in High-Order Uncertain Models](https://mlsanity.com/paper/2402.18946/) (2024)
- [Safe Uncertainty-Aware Learning of Robotic Suturing](https://mlsanity.com/paper/2505.16596/) (2025)
- [ProBF: Learning Probabilistic Safety Certificates with Barrier Functions](https://mlsanity.com/paper/2112.12210/) (2021)
- [Exploiting Differential Flatness for Efficient Learning-based Model Predictive Control of Constrained Multi-Input Control Affine Systems](https://mlsanity.com/paper/2604.24706/) (2026)

## Abstract (arXiv)

This paper presents a method to design a min-norm Control Lyapunov Function (CLF)-based stabilizing controller for a control-affine system with uncertain dynamics using Gaussian Process (GP) regression. In order to estimate both state and input-dependent model uncertainty, we propose a novel compound kernel that captures the control-affine nature of the problem. Furthermore, by the use of GP Upper Confidence Bound analysis, we provide probabilistic bounds of the regression error, leading to the formulation of a CLF-based stability chance constraint which can be incorporated in a min-norm optimization problem. We show that this resulting optimization problem is convex, and we call it Gaussian Process-based Control Lyapunov Function Second-Order Cone Program (GP-CLF-SOCP). The data-collection process and the training of the GP regression model are carried out in an episodic learning fashion. We validate the proposed algorithm and controller in numerical simulations of an inverted pendulum and a kinematic bicycle model, resulting in stable trajectories which are very similar to the ones obtained if we actually knew the true plant dynamics.