When Freshness Is Not Enough: Distribution-Aware Age of Information for Networked LQR Control

2026-06-02

AI Summary

This study addresses the inadequacy of traditional age-of-information (AoI) metrics—based solely on average AoI—in capturing closed-loop LQR tracking performance, as they lack grounding in control theory. Focusing on scalar linear time-invariant systems with delayed intermittent updates, the authors reformulate the infinite-horizon LQR problem as an optimization over the distribution of update intervals. They establish, for the first time from a control-theoretic perspective, that control performance depends critically on higher-order and even exponential moments of the inter-update interval distribution, not merely its mean. Leveraging stochastic control, LQR optimization, and moment analysis, the work demonstrates that distinct scheduling policies yielding identical average AoI can result in markedly different control performance. This phenomenon is validated using real-world NGSIM vehicle trajectory data, underscoring the necessity of distribution-aware AoI metrics and full distributional modeling in control-oriented network design.

Abstract

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.

Problem

• Age of Information
• Networked Control
• LQR
• Inter-scheduling Intervals
• Closed-loop Performance

Innovation

• Age of Information
• LQR control
• distribution-aware scheduling
• inter-scheduling intervals
• higher-order moments