有噪声通信链路上线性系统镇定的任意时刻容量的必要性和充分性第一部分：标量系统
The necessity and sufficiency of anytime capacity for stabilization of a linear system over a noisy communication link Part I: scalar systems
摘要：
我们回顾如何香农的经典概念的能力是不够的，以表征一个嘈杂的通信信道，如果该信道是用来作为一个反馈回路的一部分，以稳定一个不稳定的标量线性系统。虽然经典的能力是不够的，另一种意义上的能力（参数化的可靠性）被称为“随时容量”是必要的一个不稳定的过程的稳定。所需的速率由不稳定系统增益的对数给出，所需的可靠性来自所需的稳定性。这个必要性的结果的一个后果是一个连续的一般化的Schalkwijk/Kailath计划的AWGN信道上的反馈通信。在编码器和解码器之间的足够丰富的信息模式的情况下，足够的随时容量也被证明是足够的存在一个稳定的控制器。这些充分性的结果，然后推广到有噪声的意见，延迟的控制行动的情况下，没有任何显式的观察员和控制器之间的反馈。这两个必要条件和充分条件也被推广到连续时间系统。最后，我们讨论了一个层次的沟通问题的难度，以及如何建立这些结果稳定的问题，坐在该层次结构的评论。
英文摘要：
We review how Shannon's classical notion of capacity is not enough to characterize a noisy communication channel if the channel is intended to be used as part of a feedback loop to stabilize an unstable scalar linear system. While classical capacity is not enough, another sense of capacity (parametrized by reliability) called ``anytime capacity'' is shown to be necessary for the stabilization of an unstable process. The required rate is given by the log of the unstable system gain and the required reliability comes from the sense of stability desired. A consequence of this necessity result is a sequential generalization of the Schalkwijk/Kailath scheme for communication over the AWGN channel with feedback. In cases of sufficiently rich information patterns between the encoder and decoder, adequate anytime capacity is also shown to be sufficient for there to exist a stabilizing controller. These sufficiency results are then generalized to cases with noisy observations, delayed control actions, and without any explicit feedback between the observer and the controller. Both necessary and sufficient conditions are extended to continuous time systems as well. We close with comments discussing a hierarchy of difficulty for communication problems and how these results establish where stabilization problems sit in that hierarchy.
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