用科普曼算子建模系统不确定性，实现鲁棒非线性观测器设计。
Uncertainty Modelling and Robust Observer Synthesis using the Koopman Operator
- 基于科普曼算子将非线性系统转为近似线性模型
- 在频域量化多系统间制造差异，实现鲁棒观测器设计
- 适用于电机驱动等存在制造差异的工业场景
本文提出一种基于科普曼算子的鲁棒非线性观测器设计方法，适用于一组由科普曼算子建模的系统。科普曼算子可将非线性系统表示为无限维线性系统，其有限维近似可通过数据直接识别，从而得到非线性系统的近似线性模型。该方法利用此线性特性，在频域中量化一组科普曼模型间的不确定性。基于该不确定性模型，采用混合$/mathcal{H}_2$-$/mathcal{H}_ ty$最优控制技术，合成鲁棒的非线性科普曼观测器。通过几十个电机驱动组成的群体实验验证了该方法的有效性，成功在频域表征制造差异，并实现了鲁棒观测器的合成。
原文摘要 · Abstract (English)
This paper proposes a robust nonlinear observer synthesis method for a population of systems modelled using the Koopman operator. The Koopman operator allows nonlinear systems to be rewritten as infinite-dimensional linear systems. A finite-dimensional approximation of the Koopman operator can be identified directly from data, yielding an approximately linear model of a nonlinear system. The proposed observer synthesis method is made possible by this linearity that in turn allows uncertainty within a population of Koopman models to be quantified in the frequency domain. Using this uncertainty model, linear robust control techniques are used to synthesize robust nonlinear Koopman observers. A population of several dozen motor drives is used to experimentally demonstrate the proposed method. Manufacturing variation is characterized in the frequency domain, and a robust Koopman observer is synthesized using mixed $\mathcal{H}_2$-$\mathcal{H}_\infty$ optimal control.
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