Stable Gaussian process based tracking control of Euler–Lagrange systems

Thomas Beckers, Dana Kulić, Sandra Hirche

Research output: Contribution to journalArticleResearchpeer-review

11 Citations (Scopus)


Perfect tracking control for real-world Euler–Lagrange systems is challenging due to uncertainties in the system model and external disturbances. The magnitude of the tracking error can be reduced either by increasing the feedback gains or improving the model of the system. The latter is clearly preferable as it allows to maintain good tracking performance at low feedback gains. However, accurate models are often difficult to obtain. In this article, we address the problem of stable high-performance tracking control for unknown Euler–Lagrange systems. In particular, we employ Gaussian Process regression to obtain a data-driven model that is used for the feed-forward compensation of unknown dynamics of the system. The model fidelity is used to adapt the feedback gains allowing low feedback gains in state space regions of high model confidence. The proposed control law guarantees a globally bounded tracking error with a specific probability. Simulation studies demonstrate the superiority over state of the art tracking control approaches.

Original languageEnglish
Pages (from-to)390-397
Number of pages8
Publication statusPublished - 1 May 2019
Externally publishedYes


  • Adaptive system and control
  • Data-based control
  • Nonparametric methods
  • Robotic manipulators
  • Stability of nonlinear systems
  • Stochastic control

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