11 research outputs found
Stable Gaussian Process based Tracking Control of Lagrangian Systems
High performance tracking control can only be achieved if a good model of the
dynamics is available. However, such a model is often difficult to obtain from
first order physics only. In this paper, we develop a data-driven control law
that ensures closed loop stability of Lagrangian systems. For this purpose, we
use Gaussian Process regression for the feed-forward compensation of the
unknown dynamics of the system. The gains of the feedback part are adapted
based on the uncertainty of the learned model. Thus, the feedback gains are
kept low as long as the learned model describes the true system sufficiently
precisely. We show how to select a suitable gain adaption law that incorporates
the uncertainty of the model to guarantee a globally bounded tracking error. A
simulation with a robot manipulator demonstrates the efficacy of the proposed
control law.Comment: Please cite the conference paper. arXiv admin note: text overlap with
arXiv:1806.0719
Episodic Gaussian Process-Based Learning Control with Vanishing Tracking Errors
Due to the increasing complexity of technical systems, accurate first
principle models can often not be obtained. Supervised machine learning can
mitigate this issue by inferring models from measurement data. Gaussian process
regression is particularly well suited for this purpose due to its high
data-efficiency and its explicit uncertainty representation, which allows the
derivation of prediction error bounds. These error bounds have been exploited
to show tracking accuracy guarantees for a variety of control approaches, but
their direct dependency on the training data is generally unclear. We address
this issue by deriving a Bayesian prediction error bound for GP regression,
which we show to decay with the growth of a novel, kernel-based measure of data
density. Based on the prediction error bound, we prove time-varying tracking
accuracy guarantees for learned GP models used as feedback compensation of
unknown nonlinearities, and show to achieve vanishing tracking error with
increasing data density. This enables us to develop an episodic approach for
learning Gaussian process models, such that an arbitrary tracking accuracy can
be guaranteed. The effectiveness of the derived theory is demonstrated in
several simulations
Real-time Uncertainty Decomposition for Online Learning Control
Safety-critical decisions based on machine learning models require a clear
understanding of the involved uncertainties to avoid hazardous or risky
situations. While aleatoric uncertainty can be explicitly modeled given a
parametric description, epistemic uncertainty rather describes the presence or
absence of training data. This paper proposes a novel generic method for
modeling epistemic uncertainty and shows its advantages over existing
approaches for neural networks on various data sets. It can be directly
combined with aleatoric uncertainty estimates and allows for prediction in
real-time as the inference is sample-free. We exploit this property in a
model-based quadcopter control setting and demonstrate how the controller
benefits from a differentiation between aleatoric and epistemic uncertainty in
online learning of thermal disturbances.Comment: Submitted to ICRL 2021, updated after rebuttal perio