Prediction with Approximated Gaussian Process Dynamical Models
- URL: http://arxiv.org/abs/2006.14551v2
- Date: Tue, 30 Nov 2021 15:38:25 GMT
- Title: Prediction with Approximated Gaussian Process Dynamical Models
- Authors: Thomas Beckers and Sandra Hirche
- Abstract summary: We present approximated GPDMs which are Markov and analyze their control theoretical properties.
The outcomes are illustrated with numerical examples that show the power of the approximated models.
- Score: 7.678864239473703
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The modeling and simulation of dynamical systems is a necessary step for many
control approaches. Using classical, parameter-based techniques for modeling of
modern systems, e.g., soft robotics or human-robot interaction, is often
challenging or even infeasible due to the complexity of the system dynamics. In
contrast, data-driven approaches need only a minimum of prior knowledge and
scale with the complexity of the system. In particular, Gaussian process
dynamical models (GPDMs) provide very promising results for the modeling of
complex dynamics. However, the control properties of these GP models are just
sparsely researched, which leads to a "blackbox" treatment in modeling and
control scenarios. In addition, the sampling of GPDMs for prediction purpose
respecting their non-parametric nature results in non-Markovian dynamics making
the theoretical analysis challenging. In this article, we present approximated
GPDMs which are Markov and analyze their control theoretical properties. Among
others, the approximated error is analyzed and conditions for boundedness of
the trajectories are provided. The outcomes are illustrated with numerical
examples that show the power of the approximated models while the the
computational time is significantly reduced.
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