提出异方差高斯过程后验分布的精确理论分析方法
Theoretical Analysis of Heteroscedastic Gaussian Processes with Posterior Distributions
- 推导出异方差高斯过程后验均值、方差和累积分布的精确表达式
- 在存在未知扰动时，实现了对系统约束的概率满足控制
- 适用于需要处理不确定性和非平稳噪声的控制场景
本研究提出一种新颖的理论框架，用于分析数据驱动下识别未知系统的异方差高斯过程（HGPs）。尽管HGPs能有效处理复杂训练数据中的异方差噪声，但其后验分布不再服从多元正态分布，导致精确计算困难。本文推导出后验分布的精确均值、方差和累积分布函数。进一步将所得理论成果应用于概率约束跟踪控制器：当HGPs识别出系统中的未知扰动后，控制器仍可处理系统在扰动存在下的概率约束问题。
原文摘要 · Abstract (English)
This study introduces a novel theoretical framework for analyzing heteroscedastic Gaussian processes (HGPs) that identify unknown systems in a data-driven manner. Although HGPs effectively address the heteroscedasticity of noise in complex training datasets, calculating the exact posterior distributions of the HGPs is challenging, as these distributions are no longer multivariate normal. This study derives the exact means, variances, and cumulative distributions of the posterior distributions. Furthermore, the derived theoretical findings are applied to a chance-constrained tracking controller. After an HGP identifies an unknown disturbance in a plant system, the controller can handle chance constraints regarding the system despite the presence of the disturbance.
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