# Stable Gaussian Process based Tracking Control of Euler-Lagrange Systems

**Authors:** Thomas Beckers, Dana Kulić, Sandra Hirche  
**arXiv:** [1806.07190](https://arxiv.org/abs/1806.07190)  
**Date:** 2018-06-19  
**Summary page:** https://www.summarizepaper.com/en/paper/1806.07190v1/

## Key points

- Achieving perfect tracking control for real-world Euler-Lagrange systems is challenging due to uncertainties and external disturbances.
- Increasing feedback gains may not always be effective; improving the system model can lead to better tracking performance at lower feedback gains.
- Authors Thomas Beckers, Dana Kulić, and Sandra Hirche propose a high-performance tracking control strategy using Gaussian Process Regression (GPR) for unknown Euler-Lagrange systems.
- GPR provides estimates of uncertainties and model confidence based on proximity to training points, enabling adaptive adjustment of feedback gains.
- The proposed confidence-adaptive feedback control law ensures globally bounded tracking error with a specific probability, offering a robust solution for real-world applications.

## Summary

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In the field of control systems, achieving perfect tracking control for real-world Euler-Lagrange systems poses a significant challenge due to uncertainties in the system model and external disturbances. One common approach to reducing tracking error is by increasing feedback gains, but this may not always be effective or efficient. Alternatively, improving the model of the system can lead to better tracking performance at lower feedback gains. However, obtaining accurate models can be difficult in practice. In their article titled "Stable Gaussian Process based Tracking Control of Euler-Lagrange Systems," authors Thomas Beckers, Dana Kulić, and Sandra Hirche address this challenge by proposing a high-performance tracking control strategy for unknown Euler-Lagrange systems. The key innovation lies in employing Gaussian Process Regression (GPR) to develop a data-driven model that compensates for the unknown dynamics of the system through feed-forward control. One of the advantages of using GPR is that it not only provides estimates of uncertainties but also offers a measure of model confidence based on proximity to training points. This allows for adaptive adjustment of feedback gains depending on the fidelity of the model, enabling low feedback gains in regions of high confidence within the state space. Additionally, the authors investigate the stability of GP-based tracking control for Euler-Lagrange systems. The proposed confidence-adaptive feedback control law ensures globally bounded tracking error with a specific probability, offering a robust solution for real-world applications. Through simulation studies, Beckers et al. demonstrate the effectiveness and superiority of their approach compared to existing state-of-the-art tracking control methods. Overall, this work contributes valuable insights into enhancing tracking performance in uncertain Euler-Lagrange systems using data-driven modeling techniques like GPR, paving the way for more reliable and efficient control strategies in practical applications.