arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2402.04665eess.SYcs.SY
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基于高斯过程的非线性移动地平线估计

Gaussian Process-Based Nonlinear Moving Horizon Estimation

Tobias M. Wolff, Victor G. Lopez, Matthias A. Müller

AI总结:

本文针对未知非线性系统提出一种基于高斯过程的移动地平线估计框架,利用GP后验均值近似系统动态并用后验方差设计代价函数权重矩阵,证明了该方案的鲁棒稳定性及增量输入/输出到状态稳定性的充分条件,仿真表明其性能优于标准代价函数。

摘要:

在本文中,我们针对未知非线性系统提出了一种新颖的基于高斯过程的移动地平线估计(MHE)框架。一方面,我们通过学习到的高斯过程(GPs)的后验均值来近似系统动态。另一方面,我们利用高斯过程的后验方差来设计MHE代价函数中的权重矩阵,并考虑所学系统动态中的不确定性。数据收集和超参数的调整均离线完成。我们使用基于Lyapunov的证明技术证明了基于GP的MHE方案的鲁棒稳定性。此外,作为额外贡献,我们推导出了一个充分条件,在该条件下,当使用机器学习等技术近似系统动态时,增量输入/输出到状态稳定性(一种非线性可检测性概念)得以保持。最后,我们在两个仿真案例研究中展示了基于GP的MHE方案的性能,并说明了与标准代价函数相比,所选的权重矩阵如何带来性能的提升。

英文摘要:

In this paper, we propose a novel Gaussian process-based moving horizon estimation (MHE) framework for unknown nonlinear systems. On the one hand, we approximate the system dynamics by the posterior means of the learned Gaussian processes (GPs). On the other hand, we exploit the posterior variances of the Gaussian processes to design the weighting matrices in the MHE cost function and account for the uncertainty in the learned system dynamics. The data collection and the tuning of the hyperparameters are done offline. We prove robust stability of the GP-based MHE scheme using a Lyapunov-based proof technique. Furthermore, as additional contribution, we derive a sufficient condition under which incremental input/output-to-state stability (a nonlinear detectability notion) is preserved when approximating the system dynamics using, e.g., machine learning techniques. Finally, we illustrate the performance of the GP-based MHE scheme in two simulation case studies and show how the chosen weighting matrices can lead to an improved performance compared to standard cost functions.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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