论文标题
使用近似高斯工艺动态模型的预测
Prediction with Approximated Gaussian Process Dynamical Models
论文作者
论文摘要
动态系统的建模和仿真是许多控制方法的必要步骤。使用基于参数的经典技术来建模现代系统，例如软机器人技术或人类机器人的相互作用，由于系统动力学的复杂性，通常会具有挑战性甚至不可行。相比之下，数据驱动的方法仅需要至少与系统复杂性有关的先验知识和规模。特别是，高斯工艺动力学模型（GPDMS）为复杂动力学的建模提供了非常有希望的结果。但是，这些GP模型的控制特性只是稀疏的研究，这在建模和控制场景中导致了“黑盒”处理。此外，GPDM用于预测目的的采样尊重其非参数性质会导致非马克维亚动力学，从而使理论分析具有挑战性。在本文中，我们介绍了Markov的近似GPDM，并分析了它们的控制理论特性。除其他外，分析了近似误差，并提供了轨迹界限的条件。结果用数值示例说明了结果，这些示例显示了近似模型的功能，而计算时间大大减少了。
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.
