Title: A Linear Programming Framework for Optimal Event-Triggered LQG Control Show Chinese title

Title: 一种用于最优事件触发LQG控制的线性规划框架

Abstract: This letter explores intelligent scheduling of sensor-to-controller communication in networked control systems, particularly when data transmission incurs a cost. While the optimal controller in a standard linear quadratic Gaussian (LQG) setup can be computed analytically, determining the optimal times to transmit sensor data remains computationally and analytically challenging. We show that, through reformulation and the introduction of auxiliary binary variables, the scheduling problem can be cast as a computationally efficient mixed-integer linear program (MILP). This formulation not only simplifies the analysis but also reveals structural insights and provides clear decision criteria at each step. Embedding the approach within a model predictive control (MPC) framework enables dynamic adaptation, and we prove that the resulting scheduler performs at least as well as any deterministic strategy (e.g., periodic strategy). Simulation results further demonstrate that our method consistently outperforms traditional periodic scheduling. Show Chinese abstract

Abstract: 这封信探讨了在网络化控制系统中传感器到控制器通信的智能调度，特别是在数据传输产生成本的情况下。 虽然在标准线性二次高斯（LQG）设置中的最优控制器可以解析计算，但确定传输传感器数据的最佳时间仍然在计算和分析上具有挑战性。 我们表明，通过重新表述和引入辅助二进制变量，调度问题可以转化为计算效率高的混合整数线性规划（MILP）。 这种公式不仅简化了分析，还揭示了结构上的洞察力，并在每一步提供了明确的决策标准。 将该方法嵌入模型预测控制（MPC）框架中可以实现动态适应，我们证明所得到的调度器至少与任何确定性策略（例如，周期性策略）一样有效。 仿真结果进一步表明，我们的方法始终优于传统的周期性调度。