In this chapter, we study the consistency of the value of information$\unicode{x2014}$a semantic metric that claims to determine the right piece of information in networked control systems tasks$\unicode{x2014}$in a lossy and delayed communication regime. Our analysis begins with a focus on state estimation, and subsequently extends to feedback control. To that end, we make a causal tradeoff between the packet rate and the mean square error. Associated with this tradeoff, we demonstrate the existence of an optimal policy profile, comprising a symmetric threshold scheduling policy based on the value of information for the encoder and a non-Gaussian linear estimation policy for the decoder. Our structural results assert that the scheduling policy is expressible in terms of $3d-1$ variables related to the source and the channel, where $d$ is the time delay, and that the estimation policy incorporates no residual related to signaling. We then construct an optimal control policy by exploiting the separation principle.

翻译：本章研究信息价值（一种声称能确定网络化控制系统任务中正确信息片段的语义度量）在有损和延迟通信场景下的一致性。我们的分析首先聚焦于状态估计，随后扩展到反馈控制。为此，我们在包速率与均方误差之间建立了因果权衡关系。与此权衡相关，我们证明了存在一个最优策略组合，包括基于信息价值的编码器对称阈值调度策略与解码器非高斯线性估计策略。结构结果表明，该调度策略可表示为与信源和信道相关的$3d-1$个变量（其中$d$为时间延迟），且估计策略不包含与信令相关的残差。随后我们利用分离原理构建了最优控制策略。