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arXiv 2009.05253eess.SYcs.SYmath.OC
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结合先验知识与数据进行鲁棒控制器设计

Combining Prior Knowledge and Data for Robust Controller Design

Julian Berberich, Carsten W. Scherer, Frank Allgöwer

AI总结:

提出融合未知LTI系统数据与系统矩阵或不确定性先验知识的鲁棒控制器设计框架,利用LMI准则和学习乘子保证稳定性与性能,并扩展到含噪输出反馈及非线性不确定性。

摘要:

我们提出了一个框架,用于系统地将未知线性时不变系统的数据与关于系统矩阵或不确定性的先验知识相结合,以进行鲁棒控制器设计。我们的方法产生了基于线性矩阵不等式(LMI)的可行性准则,这些准则为所有与先验知识和可用数据一致的闭环系统鲁棒地保证稳定性和性能。设计过程依赖于通过先验知识推断以及从测量数据中学习得到的乘子的组合,其中对于后者采用了一种新颖且统一的扰动描述。虽然本文大部分内容聚焦于线性系统和输入-状态测量,但我们也提供了向基于含噪输入-输出数据并针对非线性不确定性的鲁棒输出反馈设计的扩展。我们通过数值算例说明,我们的方法为同时利用先验知识和数据提供了一个灵活的框架,从而与数据驱动控制的黑箱方法相比,降低了保守性并显著提升了性能。

英文摘要:

We present a framework for systematically combining data of an unknown linear time-invariant system with prior knowledge on the system matrices or on the uncertainty for robust controller design. Our approach leads to linear matrix inequality (LMI) based feasibility criteria which guarantee stability and performance robustly for all closed-loop systems consistent with the prior knowledge and the available data. The design procedures rely on a combination of multipliers inferred via prior knowledge and learnt from measured data, where for the latter a novel and unifying disturbance description is employed. While large parts of the paper focus on linear systems and input-state measurements, we also provide extensions to robust output-feedback design based on noisy input-output data and against nonlinear uncertainties. We illustrate through numerical examples that our approach provides a flexible framework for simultaneously leveraging prior knowledge and data, thereby reducing conservatism and improving performance significantly if compared to black-box approaches to data-driven control.

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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