Feedback Stabilization Over Signal-to-Noise Ratio Constrained Channels
Feedback Stabilization Over Signal-to-Noise Ratio Constrained Channels
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DOI：
10.1109/tac.2007.902739
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发表时间：
2007-08
影响因子：
6.8
通讯作者：
J. Braslavsky;R. Middleton;J. Freudenberg
中科院分区：
文献类型：
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作者：
J. Braslavsky;R. Middleton;J. Freudenberg
最近有显着的兴趣反馈稳定问题的通信约束，包括可用的数据速率的约束。信噪比（SNR）的限制是数据速率限制出现的一种方式，是本文的重点。在连续和离散时间设置中，我们表明，有能力稳定的SNR约束的信道上使用有限维线性时不变（LTI）反馈的不稳定植物的限制。在状态反馈的情况下，或输出反馈与无延迟，最小相位工厂，这些限制实际上精确匹配那些可能已经推断出的考虑相关的理想香农容量数据速率在相同的信道。在LTI输出反馈的情况下，额外的限制示出适用于如果植物是nonminimum相位。在这种情况下，我们表明，对于一个连续时间的非最小相位植物，一个周期性的线性时变反馈方案与快速采样可以用来恢复原始的SNR要求的鲁棒性的成本。所提出的框架固有地捕获信道噪声的影响，在一个简单的配方适合于传统的LTI控制性能和鲁棒性分析，并有可能处理时间延迟和带宽的限制，在各种控制通信链路的问题。
There has recently been significant interest in feedback stabilization problems with communication constraints including constraints on the available data rate. Signal-to-noise ratio (SNR) constraints are one way in which data-rate limits arise, and are the focus of this paper. In both continuous and discrete-time settings, we show that there are limitations on the ability to stabilize an unstable plant over a SNR constrained channel using finite-dimensional linear time invariant (LTI) feedback. In the case of state feedback, or output feedback with a delay-free, minimum phase plant, these limitations in fact match precisely those that might have been inferred by considering the associated ideal Shannon capacity data rate over the same channel. In the case of LTI output feedback, additional limitations are shown to apply if the plant is nonminimum phase. In this case, we show that for a continuous-time nonminimum phase plant, a periodic linear time varying feedback scheme with fast sampling may be used to recover the original SNR requirement at the cost of robustness properties. The proposed framework inherently captures channel noise effects in a simple formulation suited to conventional LTI control performance and robustness analysis, and has potential to handle time delays and bandwidth constraints in a variety of control over communication links problems.