在间歇反馈下，对称调度最优，可实现控制与调度分离。
Separation is Optimal for LQR under Intermittent Feedback
- 采用对称调度策略，解耦控制与通信决策
- 最优调度为基于累积扰动的阈值规则
- 适用于随机扰动下的资源受限控制系统
研究了在平均通信速率约束下，具有间歇状态反馈的标量线性系统有限时域线性二次调节问题。在此场景中，调度策略与控制器因双重效应而耦合：传输决策影响未来估计误差，控制动作又改变调度可用信息。现有方法常通过限制对称调度策略来恢复可处理性，但该限制是否最优尚不明确。本文证明，在独立同分布零均值扰动下，对称策略是最优的。因此，通信约束下的LQR问题具有分离结构：最优控制器为独立于调度策略的线性反馈律，最优调度器可通过动态规划获得。进一步表明，最优调度规则是基于自上一次更新以来累积扰动的对称阈值策略。
原文摘要 · Abstract (English)
We study finite-horizon linear-quadratic regulation of a scalar linear system with intermittent state feedback under an average communication-rate constraint. In this setting, the scheduling policy and controller are generally coupled through the dual effect: transmission decisions shape future estimation errors, while control actions influence the information available for scheduling. Existing treatments often recover tractability by restricting attention to symmetric scheduling policies, but the optimality of this restriction has remained unclear. We show that, for i.i.d. zero-mean disturbances, symmetric policies are optimal. Consequently, the communication-constrained LQR problem admits a separation structure. The optimal controller is a linear feedback law independent of the scheduling policy, while the optimal scheduler is obtained from a dynamic program. We further show that the optimal scheduling rule is a symmetric threshold policy in the accumulated disturbance since the most recent update.
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