论文标题
关节传感器和执行器调度的分离定理，并保证了性能界限
A Separation Theorem for Joint Sensor and Actuator Scheduling with Guaranteed Performance Bounds
论文作者
论文摘要
我们研究了与线性动力学系统共同设计稀疏传感器和执行器计划的问题，同时保证了近似完全感应/驱动设置的控制/估计性能。我们进一步证明了一个分离原理，表明该问题可以分别分开找到传感器和执行器时间表。但是，结果表明，对于时间不变的传感器/执行器计划，在多项式甚至准多项式时间中无法有效地解决或近似。取而代之的是，我们为具有保证的近似边界的时变传感器/执行器计划开发确定性多项式算法。我们的主要结果是提供一个多项式的联合执行器和传感器时间表，该时间表平均在每个时间步骤中仅选择恒定数量的传感器和执行器，而与系统的尺寸无关。关键的想法是稀疏Gramians的可控性和可观察性，同时为Hankel单数值提供近似保证。这个想法的灵感来自理论计算机科学文献有关稀疏的最新结果。
We study the problem of jointly designing a sparse sensor and actuator schedule for linear dynamical systems while guaranteeing a control/estimation performance that approximates the fully sensed/actuated setting. We further prove a separation principle, showing that the problem can be decomposed into finding sensor and actuator schedules separately. However, it is shown that this problem cannot be efficiently solved or approximated in polynomial, or even quasi-polynomial time for time-invariant sensor/actuator schedules; instead, we develop deterministic polynomial-time algorithms for a time-varying sensor/actuator schedule with guaranteed approximation bounds. Our main result is to provide a polynomial-time joint actuator and sensor schedule that on average selects only a constant number of sensors and actuators at each time step, irrespective of the dimension of the system. The key idea is to sparsify the controllability and observability Gramians while providing approximation guarantees for Hankel singular values. This idea is inspired by recent results in theoretical computer science literature on sparsification.
