Prediction With Approximated Gaussian Process Dynamical Models

• 成果类型: Article
• 署名作者: Beckers, Thomas; Hirche, Sandra
• 署名单位: University of Pennsylvania; Technical University of Munich
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3131988
• 发表日期: 2022
• 页码: 6460-6473
• 关键词: Data-based control; Gaussian processes (GPs); Learning systems; nonparametric methods; probabilistic models; probabilistic simulation; stochastic modeling

摘要

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, are 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 nonparametric 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 computational time is significantly reduced.