Value of Information in Feedback Control: Quantification
Value of Information in Feedback Control: Quantification
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DOI：
10.1109/tac.2021.3113472
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发表时间：
2018-12
影响因子：
6.8
通讯作者：
T. Soleymani;J. Baras;S. Hirche
中科院分区：
文献类型：
--
作者：
T. Soleymani;J. Baras;S. Hirche
虽然在网络控制系统中传输包含感官信息的数据包提高了调节质量，但从通信的角度来看，它确实有代价。因此，只有在这种数据包在成本效益分析意义上有价值的情况下才传输它是合理的。然而，事实是，到目前为止，人们对信息的这种价值及其与传统事件触发通信的联系知之甚少。在本文中，我们通过将事件触发器和控制器作为两个分布式决策者，在分组速率和调节成本之间制定速率调节权衡来研究网络控制系统的这一固有特性，并表明基于这种权衡的信息评估是可想象和可量化的。特别是，我们描述了速率调节权衡中的平衡，并将那里的信息${\rm{VoI}}_k$的值量化为所谓的值函数中与可在每次$k$传达给控制器的一条感官信息有关的变化。我们证明了对于一个多维高斯—马尔可夫过程，${\rm{VoI}}_k$是事件触发点状态估计与控制器状态估计差异的对称函数，并且只有当${\rm{VoI}}_k$非负时，包含$k$时刻感官信息的数据包才应该传输到控制器。此外，我们讨论了${\rm{VoI}}_k$可以以任意精度计算，并且可以用具有性能保证的封闭式二次函数来近似。
Although transmission of a data packet containing sensory information in a networked control system improves the quality of regulation, it has indeed a price from the communication perspective. It is, therefore, rational that such a data packet be transmitted only if it is valuable in the sense of a cost-benefit analysis. Yet, the fact is that little is known so far about this valuation of information and its connection with traditional event-triggered communication. In the present article, we study this intrinsic property of networked control systems by formulating a rate-regulation trade-off between the packet rate and the regulation cost with an event trigger and a controller as two distributed decision makers, and show that the valuation of information is conceivable and quantifiable grounded on this trade-off. In particular, we characterize an equilibrium in the rate-regulation trade-off, and quantify the value of information ${\rm{VoI}}_k$ there as the variation in a so-called value function with respect to a piece of sensory information that can be communicated to the controller at each time $k$. We prove that, for a multi-dimensional Gauss--Markov process, ${\rm{VoI}}_k$ is a symmetric function of the discrepancy between the state estimates at the event trigger and the controller, and that a data packet containing sensory information at time $k$ should be transmitted to the controller only if ${\rm{VoI}}_k$ is nonnegative. Moreover, we discuss that ${\rm{VoI}}_k$ can be computed with arbitrary accuracy, and that it can be approximated by a closed-form quadratic function with a performance guarantee.