# Feedback Linearization based on Gaussian Processes with event-triggered Online Learning

arXiv: https://arxiv.org/abs/1911.06565 · HTML: https://mlsanity.com/paper/1911.06565/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Nov 2019.

## Built on by (most cited first, 24 of 24)

- [Efficient Exploration in Continuous-time Model-based Reinforcement Learning](https://mlsanity.com/paper/2310.19848/) (2023)
- [Robust Uncertainty Bounds in Reproducing Kernel Hilbert Spaces: A Convex Optimization Approach](https://mlsanity.com/paper/2104.09582/) (2021)
- [Can Learning Deteriorate Control? Analyzing Computational Delays in Gaussian Process-Based Event-Triggered Online Learning](https://mlsanity.com/paper/2305.08169/) (2023)
- [Uniform Error and Posterior Variance Bounds for Gaussian Process Regression with Application to Safe Control](https://mlsanity.com/paper/2101.05328/) (2021)
- [Event-Triggered Time-Varying Bayesian Optimization](https://mlsanity.com/paper/2208.10790/) (2022)
- [Policy Gradient Converges to the Globally Optimal Policy for Nearly Linear-Quadratic Regulators](https://mlsanity.com/paper/2303.08431/) (2023)
- [Cooperative Learning with Gaussian Processes for Euler-Lagrange Systems Tracking Control under Switching Topologies](https://mlsanity.com/paper/2402.03048/) (2024)
- [Structure-Preserving Learning Using Gaussian Processes and Variational Integrators](https://mlsanity.com/paper/2112.05451/) (2021)
- [Learning-Based Optimal Control with Performance Guarantees for Unknown Systems with Latent States](https://mlsanity.com/paper/2303.17963/) (2023)
- [Exploring the Links between the Fundamental Lemma and Kernel Regression](https://mlsanity.com/paper/2403.05368/) (2024)
- [Distributed Event-Based Learning via ADMM](https://mlsanity.com/paper/2405.10618/) (2024)
- [Networked Online Learning for Control of Safety-Critical Resource-Constrained Systems based on Gaussian Processes](https://mlsanity.com/paper/2202.11491/) (2022)
- [Recursively Feasible Probabilistic Safe Online Learning with Control Barrier Functions](https://mlsanity.com/paper/2208.10733/) (2022)
- [Personalized Rehabilitation Robotics based on Online Learning Control](https://mlsanity.com/paper/2110.00481/) (2021)
- [Data driven feedback linearization of nonlinear control systems via Lie derivatives and stacked regression approach](https://mlsanity.com/paper/2508.13241/) (2025)
- [Concurrent Learning Based Tracking Control of Nonlinear Systems using Gaussian Process](https://mlsanity.com/paper/2106.00910/) (2021)
- [Improving the Performance of Robust Control through Event-Triggered Learning](https://mlsanity.com/paper/2207.14252/) (2022)
- [Episodic Gaussian Process-Based Learning Control with Vanishing Tracking Errors](https://mlsanity.com/paper/2307.04415/) (2023)
- [Decentralized Event-Triggered Online Learning for Safe Consensus of Multi-Agent Systems with Gaussian Process Regression](https://mlsanity.com/paper/2402.03174/) (2024)
- [Learning Dynamics from Infrequent Output Measurements for Uncertainty-Aware Optimal Control](https://mlsanity.com/paper/2512.08013/) (2025)
- [Data-driven Control with Real-time Uncertainty Compensation for Multi-Fuel Engines](https://mlsanity.com/paper/2606.16171/) (2026)
- [Event-triggered Control and Online Learning for Networked Systems under Computational Delays](https://mlsanity.com/paper/2608.29576/) (2026)
- [COIN-GP: Cooperative Online Learning in Networked Distributed Systems with Partial Measurements via Gaussian Process Regression](https://mlsanity.com/paper/2609.20598/) (2026)
- [Learning Neural Feedback Linearization for Data-driven Systems via Augmented Lagrangian](https://mlsanity.com/paper/2609.25163/) (2026)

## Abstract (arXiv)

Combining control engineering with nonparametric modeling techniques from machine learning allows to control systems without analytic description using data-driven models. Most existing approaches separate learning, i.e. the system identification based on a fixed dataset, and control, i.e. the execution of the model-based control law. This separation makes the performance highly sensitive to the initial selection of training data and possibly requires very large datasets. This article proposes a learning feedback linearizing control law using online closed-loop identification. The employed Gaussian process model updates its training data only if the model uncertainty becomes too large. This event-triggered online learning ensures high data efficiency and thereby reduces the computational complexity, which is a major barrier for using Gaussian processes under real-time constraints. We propose safe forgetting strategies of data points to adhere to budget constraint and to further increase data-efficiency. We show asymptotic stability for the tracking error under the proposed event-triggering law and illustrate the effective identification and control in simulation.