Control Over Gaussian Channels With and Without Source-Channel Separation
Control Over Gaussian Channels With and Without Source-Channel Separation
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DOI：
10.1109/tac.2019.2912255
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发表时间：
2019-09-01
影响因子：
6.8
通讯作者：
Hassibi, Babak
中科院分区：
文献类型：
--
作者：
Khina, Anatoly;Garding, Elias Riedel;Hassibi, Babak
我们考虑的问题，控制一个不稳定的线性植物与高斯干扰的加性白色高斯噪声信道的平均发射功率约束，其中的通信信号的速率可能是不同的采样率的基础植物。这种情况是很常见的，因为采样是以捕捉工厂动态的速率进行的，并且通常低于通信信道的信令速率。这种速率失配提供了通过在多个信道使用上使用编码来传送单个控制动作来提高系统性能的机会。在传统的基于分离的信源和信道编码方法中，模拟消息首先被量化为几个比特，然后被映射到信道码字，该信道码字的长度与每个采样消息的信道使用次数相称。将基于分离的方法应用于控制满足其挑战：首先，量化器需要能够放大和缩小以能够跟踪无界系统干扰，其次，信道码必须能够随时间指数地改善其对过去传输的估计，这一特性称为随时可靠性。我们实现了一个单独的计划，利用最近开发的技术控制量化反馈信道和有效的解码的任何时间可靠的代码。我们进一步提出了一种替代方案，即，执行模拟联合信源信道编码，通过这种方式完全避免了数字域。对于通信信号速率是采样率的两倍的情况下，我们采用模拟线性重复以及Shannon-Kotel'nikov映射，以显示基于分离的方案在稳定性裕度和线性二次成本方面的显着改善。我们的结论是，这样的模拟编码比分离性能更好，可以稳定所有的时刻，以及保证几乎肯定的稳定性。
We consider the problem of controlling an unstable linear plant with Gaussian disturbances over an additive white Gaussian noise channel with an average transmit power constraint, where the signaling rate of communication may be different from the sampling rate of the underlying plant. Such a situation is quite common since sampling is done at a rate that captures the dynamics of the plant and that is often lower than the signaling rate of the communication channel. This rate mismatch offers the opportunity of improving the system performance by using coding over multiple channel uses to convey a single control action. In a traditional, separation-based approach to source and channel coding, the analog message is first quantized down to a few bits and then mapped to a channel codeword whose length is commensurate with the number of channel uses per sampled message. Applying the separation-based approach to control meets its challenges: first, the quantizer needs to be capable of zooming in and out to be able to track unbounded system disturbances, and second, the channel code must be capable of improving its estimates of the past transmissions exponentially with time, a characteristic known as anytime reliability. We implement a separated scheme by leveraging recently developed techniques for control over quantized-feedback channels and for efficient decoding of anytime-reliable codes. We further propose an alternative, namely, to perform analog joint source-channel coding, by this avoiding the digital domain altogether. For the case where the communication signaling rate is twice the sampling rate, we employ analog linear repetition as well as Shannon-Kotel'nikov maps to show a significant improvement in stability margins and linear-quadratic costs over separation-based schemes. We conclude that such analog coding performs better than separation, and can stabilize all moments as well as guarantee almost-sure stability.