传输延迟、平均数据速率与输出反馈控制性能的相互作用
Interplay Between Transmission Delay, Average Data Rate, and Performance in Output Feedback Control over Digital Communication Channels
AI总结：
研究了在数字通信通道中传输延迟对线性时不变系统性能的影响，分析了所需最小平均数据速率以实现二次性能，并通过数值示例验证了结果的适用性。
摘要：
本文研究了在无噪声数字通道中传输延迟对噪声线性时不变（LTI）系统性能的影响。该速率受限通道通过因果但任意的编码器-控制器对将系统的单测量输出连接到其单控制输入。采用信息论方法分析了在通道施加已知恒定延迟时实现二次性能所需的最小平均数据速率。该下限平均数据速率被证明通过最小化定向信息率跨一组LTI滤波器和加性白色高斯噪声（AWGN）通道来下界。证明了通道中的时间延迟会增加实现一定性能水平所需的数据速率。通过数值示例验证了结果的适用性。特别是，通过模拟显示当使用最优滤波器但将AWGN通道（用于下界）替换为简单标量均匀量化器时，所得到的操作数据速率至多在下界之上约0.3 bit。
英文摘要：
The performance of a noisy linear time-invariant (LTI) plant, controlled over a noiseless digital channel with transmission delay, is investigated in this paper. The rate-limited channel connects the single measurement output of the plant to its single control input through a causal, but otherwise arbitrary, coder-controller pair. An infomation-theoretic approach is utilized to analyze the minimal average data rate required to attain the quadratic performance when the channel imposes a known constant delay on the transmitted data. This infimum average data rate is shown to be lower bounded by minimizing the directed information rate across a set of LTI filters and an additive white Gaussian noise (AWGN) channel. It is demonstrated that the presence of time delay in the channel increases the data rate needed to achieve a certain level of performance. The applicability of the results is verified through a numerical example. In particular, we show by simulations that when the optimal filters are used but the AWGN channel (used in the lower bound) is replaced by a simple scalar uniform quantizer, the resulting operational data rates are at most around 0.3 bits above the lower bounds.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
