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首页> 外文会议>Annual Allerton Conference on Communication, Control, and Computing; 20040929-1001; Monticello,IL(US) >Fundamental Limitations of Disturbance Attenuation in the Presence of Finite Capacity Feedback
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Fundamental Limitations of Disturbance Attenuation in the Presence of Finite Capacity Feedback

机译：存在有限容量反馈时扰动衰减的基本局限性

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This paper derives a fundamental limitation of performance, in the presence of finite capacity feedback. The feedback loop comprises a discrete-time, linear and time-invariant plant, a channel, an encoder and a decoder which may also embody a controller. Measurements of the plant's output must be encoded for transmission over the channel. Information, at the other end of the channel, is decoded and used to generate a control signal, which is additively disturbed by a Gaussian and stationary stochastic process. We derive an inequality of the form L_ ≥ ∑ max {0, log (| λ_i(A)|)} - C_(channel), where L_ is a measure of disturbance rejection, A is the dynamic matrix, of the state representation of the plant, and C_(channel) is the Shannon capacity of the channel. We prove that, under a sta-tionarity assumption, L_ admits a log-sensitivity integral representation. We contrast our condition with Bode's integral formula and the water-bed effect. Such comparison rests on the fact that the former is a hard limit between capacity and attenuation, while the later is a trade-off between disturbance attenuation and amplification.
机译：在有限容量反馈的情况下，本文得出了性能的基本限制。反馈回路包括离散时间，线性和时不变的工厂，信道，编码器和解码器，它们也可以体现为控制器。必须对工厂输出的测量进行编码，以便通过通道进行传输。信道另一端的信息被解码并用于生成控制信号，该信号会受到高斯和平稳随机过程的累加干扰。我们得出以下形式的不等式：L_≥∑ max {0，log（|λ_i（A）|）}-C_（channel），其中L_是状态抑制的度量，A是动态矩阵，设备，而C_（channel）是通道的香农容量。我们证明，在稳态假设下，L_接受对数敏感性积分表示。我们将条件与Bode的积分公式和水床效应进行对比。这种比较基于这样一个事实，即前者是容量和衰减之间的硬性限制，而后者是干扰衰减和放大之间的折衷。

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