A Separation Theorem for Joint Sensor and Actuator Scheduling with Guaranteed Performance Bounds
A Separation Theorem for Joint Sensor and Actuator Scheduling with Guaranteed Performance Bounds
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DOI：
10.1016/j.automatica.2020.109054
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发表时间：
2020-05
期刊：
影响因子：
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通讯作者：
Milad Siami;A. Jadbabaie
中科院分区：
文献类型：
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作者：
Milad Siami;A. Jadbabaie
我们研究的问题，共同设计一个稀疏的传感器和执行器的线性动态系统的时间表，同时保证控制/估计性能，接近完全感测/致动设置。我们进一步证明了分离原则，表明问题可以分解成单独寻找传感器和执行器的时间表。然而，它表明，这个问题不能有效地解决或近似多项式，甚至准多项式时间的时不变的传感器/执行器的时间表，相反，我们开发了确定性的多项式时间算法的时变传感器/执行器的时间表，保证近似边界。我们的主要结果是提供一个多项式时间的联合执行器和传感器的时间表，平均只选择一个恒定数量的传感器和执行器在每个时间步，无论系统的尺寸。其关键思想是稀疏的可控性和可观性Gramian，同时提供近似保证Hankel奇异值。这个想法的灵感来自于理论计算机科学文献中关于稀疏化的最新结果。
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.