AI 中文总结
研究多编码器单解码器网络控制系统的因果率失真函数这一长期未决问题，建立新的有向信息下界，证明线性编码器和解码器对优化下界的最优性，简化分析并给出相关半定规划公式。
AI 中文摘要
本文研究具有多个编码器和单个解码器的网络控制系统的因果率失真函数，这是信息与控制理论中一个长期存在的开放问题。虽然先前工作探索了单编码器和有反馈网络设置的因果率失真函数，但无反馈网络的情况仍未解决。我们建立了一个新颖的有向信息下界，这是首次为网络控制设置推导出来的。我们进一步证明了线性、独立编码器和线性解码器对于线性二次高斯（LQG）装置和二次成本优化此下界的最优性，条件是传感器在一起时能观察到完整的装置状态。通过将原始的无限维优化问题简化为有限维问题，我们的方法简化了分析。此外，我们的有向信息下界为具有边信息和奇异噪声矩阵的单编码器和单解码器设置中线性编码器的充分性提供了另一种证明，扩展了文献中的先前结果。我们给出了具有线性边信息和奇异噪声矩阵的高斯 - 马尔可夫源的因果率失真函数的半定规划公式。
英文摘要
This paper investigates the causal rate-distortion function for networked control systems with multiple encoders and a single decoder, a longstanding open problem in information and control theory. While previous work has explored the causal rate-distortion function for single-encoder and feedback-enabled networked settings, the case of networks without feedback remains unaddressed. We establish a novel directed information lower bound, the first derived for the networked control setting. We further demonstrate the optimality of linear, independent encoders and linear decoders for optimizing this lower bound for Linear Quadratic Gaussian (LQG) plant and quadratic cost, with the condition that the full plant state is observed when sensors are sitting together. By reducing the original infinite-dimensional optimization problem to a finite-dimensional one, our approach simplifies the analysis. Additionally, our directed information lower bound provides an alternate proof for the sufficiency of linear encoders in the single encoder and single decoder setting with side information, extending prior results in the literature. We present Semidefinite Programming formulations for the causal rate distortion function of Gaussian-Markov sources with linear side information and the singular noise matrix.
Comments36 pages, 3 figures, partially presented at ISIT 2025, submitted to TAC
