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，II：向量系统
The necessity and sufficiency of anytime capacity for stabilization of a linear system over a noisy communication link, Part II: vector systems
摘要：
在第一部分中，我们回顾了香农的经典概念的能力是不足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。虽然经典的容量是不够的，一种意义上的容量（参数化的可靠性）称为“随时容量”是必要的，并在这种情况下，信道评估足够的。所需的速率是开环系统增益的对数，所需的可靠性来自所需的稳定性。即使在有噪声观测的情况下，观测器和控制器之间没有任何显式反馈，也能保持足够的精度。这建立了标量镇定问题和时滞泛反馈通信问题之间的渐近等价性。在第二部分中，建立了矢量状态的推广，并且不稳定本征值的大小起着至关重要的作用。为了处理这类系统，引入了任意时刻速率域的概念。这是通道可以支持的速率区域，同时仍然满足并行消息流的潜在不同的随时可靠性目标。所有的标量结果推广的特征值的特征值的基础上。当没有显式反馈的噪声信道输出时，不稳定系统的固有延迟告诉我们反馈延迟需要什么，同时评估信道的任意时间速率区域。一个涉及二进制擦除通道的例子是用来说明如何区分服务是需要在任何基于分离的控制架构。
英文摘要：
In part I, we reviewed how Shannon's classical notion of capacity is not sufficient 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, a sense of capacity (parametrized by reliability) called "anytime capacity" is both necessary and sufficient for channel evaluation in this context. The rate required is the log of the open-loop system gain and the required reliability comes from the desired sense of stability. Sufficiency is maintained even in cases with noisy observations and without any explicit feedback between the observer and the controller. This established the asymptotic equivalence between scalar stabilization problems and delay-universal communication problems with feedback. Here in part II, the vector-state generalizations are established and it is the magnitudes of the unstable eigenvalues that play an essential role. To deal with such systems, the concept of the anytime rate-region is introduced. This is the region of rates that the channel can support while still meeting potentially different anytime reliability targets for parallel message streams. All the scalar results generalize on an eigenvalue by eigenvalue basis. When there is no explicit feedback of the noisy channel outputs, the intrinsic delay of the unstable system tells us what the feedback delay needs to be while evaluating the anytime-rate-region for the channel. An example involving a binary erasure channel is used to illustrate how differentiated service is required in any separation-based control architecture.
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