Age of Information (AoI) has become a central metric for the design of wireless update systems, especially in applications where fresh measurements support tracking, estimation, and control. Despite its popularity, the use of mean AoI or peak AoI as a surrogate for closed-loop performance is often motivated by intuition rather than by a control-theoretic derivation. This paper examines whether minimizing the mean AoI is in fact optimal for networked control systems. For scalar linear time-invariant systems with delayed intermittent updates, we show that, under state-independent scheduling policies, the infinite-horizon LQR tracking problem reduces to an optimization over the distribution of inter-scheduling intervals. The resulting objective depends on higher-order statistical moments, and in unstable or correlated regimes on exponential moments, of the inter-scheduling process rather than only on its mean. Consequently, policies with identical mean AoI can induce substantially different tracking costs. We further extend the analysis to disturbances with exponentially decaying autocorrelation and derive equivalent cost formulations that expose the role of the full interval distribution. Finally, we validate the theory using real vehicle trajectories from the NGSIM US-101 dataset. The empirical results match the predicted performance trends, demonstrating that mean AoI alone is insufficient for control-oriented network design.

翻译：信息龄（Age of Information, AoI）已成为无线更新系统设计的核心指标，尤其在需要新鲜测量值支持跟踪、估计与控制的场景中。尽管应用广泛，将平均AoI或峰值AoI作为闭环性能替代指标的思路通常源于直觉而非控制理论的推导。本文探讨了最小化平均AoI是否确实对网络化控制系统最优。针对存在延迟间歇更新的标量线性时不变系统，我们证明在状态无关调度策略下，无限时域LQR跟踪问题可转化为对调度间隔分布的优化。所得目标函数取决于调度过程的高阶统计矩——在不稳定或相关机制下甚至取决于指数矩，而不仅限于其均值。因此，具有相同平均AoI的策略可能产生显著不同的跟踪成本。我们进一步将分析扩展至具有指数衰减自相关的扰动，并推导出揭示完整间隔分布作用的等效成本公式。最后，利用NGSIM US-101数据集中的真实车辆轨迹验证理论，实证结果与预测性能趋势一致，表明仅依赖平均AoI不足以支撑面向控制的网络设计。