Learning Stable Nonparametric Dynamical Systems with Gaussian Process Regression

@article{Xiao2020LearningSN,
  title={Learning Stable Nonparametric Dynamical Systems with Gaussian Process Regression},
  author={Wenxin Xiao and Armin Lederer and Sandra Hirche},
  journal={ArXiv},
  year={2020},
  volume={abs/2006.07868}
}
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References

SHOWING 1-10 OF 14 REFERENCES

Neural learning of vector fields for encoding stable dynamical systems

Learning control Lyapunov function to ensure stability of dynamical system-based robot reaching motions

Neural learning of stable dynamical systems based on data-driven Lyapunov candidates

A neural learning scheme that estimates stable dynamical systems from demonstrations based on a two-stage process: first, a data-driven Lyapunov function candidate is estimated, and stability is incorporated by means of a novel method to respect local constraints in the neural learning.

Uncertainty-based Human Motion Tracking with Stable Gaussian Process State Space Models

An Uncertainty-Based Control Lyapunov Approach for Control-Affine Systems Modeled by Gaussian Process

An uncertainty-based control Lyapunov function which utilizes the model fidelity estimate of a Gaussian process model to drive the system in areas near training data with low uncertainty, which maximizes the probability that the system is stabilized in the presence of power constraints using equivalence to dynamic programming.

Learning Stable Nonlinear Dynamical Systems With Gaussian Mixture Models

A learning method is proposed, which is called Stable Estimator of Dynamical Systems (SEDS), to learn the parameters of the DS to ensure that all motions closely follow the demonstrations while ultimately reaching and stopping at the target.

Local Asymptotic Stability Analysis and Region of Attraction Estimation with Gaussian Processes*

  • Armin LedererS. Hirche
  • Computer Science, Mathematics
    2019 IEEE 58th Conference on Decision and Control (CDC)
  • 2019
This work proposes a method to obtain a Lyapunov-like function for stability analysis by learning the infinite horizon cost function with a Gaussian process based on approximate dynamic programming.

A Physically-Consistent Bayesian Non-Parametric Mixture Model for Dynamical System Learning

A physically-consistent Bayesian non-parametric approach for fitting Gaussian Mixture Models (GMM) to trajectory data and a data-efficient incremental learning framework is introduced that encodes a DS from batches of trajectories, while preserving global stability.

Gaussian Processes for Machine Learning

The treatment is comprehensive and self-contained, targeted at researchers and students in machine learning and applied statistics, and deals with the supervised learning problem for both regression and classification.

Subspace identification with guaranteed stability using constrained optimization

  • S. LacyD. Bernstein
  • Mathematics
    Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301)
  • 2002
This work writes the least-squares optimization problem as a convex linear programming problem with mixed equality, quadratic, and positive-semidefinite constraints suitable for existing convex optimization codes such as SeDuMi.