Feedback control in the presence of noisy channels: "Bode-Like" fundamental limitations of performance
Feedback control in the presence of noisy channels: "Bode-Like" fundamental limitations of performance
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DOI：
10.1109/tac.2008.929361
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发表时间：
2008-08-01
影响因子：
6.8
通讯作者：
Dahleh, Munther A.
中科院分区：
文献类型：
--
作者：
Martins, Nuno C.;Dahleh, Munther A.
本文讨论的基本限制反馈信息论守恒定律和通量参数。论文分为两部分。在第一部分中，我们推导出一个守恒律，说明因果反馈不能减少外部源插入回路中的微分熵。对这一结果的一种解释是，由扰动引起的总随机性（用微分熵来衡量）不能被因果反馈所减少;它只能在时间或频率上重新分配（如果定义明确的话）。在渐近平稳性假设下，该结果具有谱表示，它构成了任意反馈的Bode不等式的扩展。我们的证明明确了因果关系的作用，以及稳定性假设如何影响最终结果。在第二部分中，我们推导出一个不等式，揭示了反馈回路必须能够传递来自两个独立来源的信息：1）物理设备的初始状态; 2）外源干扰信号。利用这一原理，我们构造了一类信息率（信息流）不等式。此外，我们推导出一个通用的性能界，这是参数化的反馈能力和参数的植物。后者是一个新的基本限制，不同于Bode的经典结果，表明有限反馈容量带来了一种新的性能界。
This paper addresses fundamental limitations of feedback using information theoretic conservation laws and flux arguments. The paper has two parts. In the first part, we derive a conservation law dictating that causal feedback cannot reduce the differential entropy inserted in the loop by external sources. An interpretation of this result is that the total randomness induced by disturbances, as measured by differential entropy, cannot be reduced by causal feedback; it can only be re-allocated in time or in frequency (if well defined). Under asymptotic stationarity assumptions, this result has a spectral representation which constitutes an extension of Bode's inequality for arbitrary feedback. Our proofs make clear the role of causality, as well as how stability assumptions impact the final result. In the second part, we derive an inequality unveiling that the feedback loop must be able to convey information originating from two independent sources:1) initial states of the physical plant; 2) exogenous disturbance signals. By using such principle, we construct a variety of information rate (information flux) inequalities. Furthermore, we derive a universal performance bound which is parameterized solely by the feedback capacity and the parameters of the plant. The latter is a new fundamental limitation, which is different from Bode's classical result, indicating that finite feedback capacity brings a new type of performance bound.