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How much uncertainty can be dealt with by feedback?

机译：反馈可以处理多少不确定性？

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摘要

Feedback is used primarily for reducing the effects of the plant uncertainty on the performance of control systems, and as such understanding the following questions is of fundamental importance: How much uncertainty can be dealt with by feedback? What are the limitations of feedback? How does the feedback performance depend quantitatively on the system uncertainty? How can the capability of feedback be enhanced if a priori information about the system structure is available? As a starting point toward answering these questions, a typical class of first-order discrete-time dynamical control systems with both unknown nonlinear structure and unknown disturbances is selected for our investigation, and some concrete answers are obtained in the paper. In particular, we find that in the space of unknown nonlinear functions, the generalized Lipschitz norm is a suitable measure for characterizing the size of the structure uncertainty, and that the maximum uncertainty that can be dealt with by the feedback mechanism is described by a ball with radius 3/2+√2 in this normed function space
机译：反馈主要用于减少设备不确定性对控制系统性能的影响，因此理解以下问题至关重要：反馈可以处理多少不确定性？反馈的局限性是什么？反馈性能如何定量地取决于系统不确定性？如果有关系统结构的先验信息可用，如何增强反馈的能力？作为回答这些问题的起点，我们选择了一类典型的同时具有未知非线性结构和未知扰动的一阶离散时间动力控制系统进行研究，并在本文中获得了一些具体答案。特别是，我们发现，在未知非线性函数的空间中，广义Lipschitz范数是表征结构不确定性大小的合适方法，并且反馈机制可以处理的最大不确定性用球来描述。在该规范函数空间中半径为3/2 +√2

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