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 tradeoff 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 tradeoff. In particular, we characterize an equilibrium in the rate-regulation tradeoff, and quantify the value of information $\text{VoI}_k$ 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, $\text{VoI}_k$ 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 $\text{VoI}_k$ is nonnegative. Moreover, we discuss that $\text{VoI}_k$ can be computed with arbitrary accuracy, and that it can be approximated by a closed-form quadratic function with a performance guarantee.
翻译:虽然在网络化控制系统中传输含有感官信息的数据集包提高了监管质量,但从通信角度来说,它的确是一个价格。因此,只有在成本效益分析意义上具有价值的情况下,才会发送这样一个数据包是合理的。然而,事实是,迄今为止对信息估值及其与传统事件触发通信的关联知之甚少。在本篇文章中,我们研究网络化控制系统的这一内在属性,方法是在数据包费率和监管成本之间制定一个节率交易,同时设定一个事件触发器和一个作为两个分布式决策者的控制器,并表明信息估值是可想象的和可量化的。特别是,我们确定费率调节交易的平衡,并量化信息值$\text{VoI ⁇ k$,因为对于每时能够传递给控制器的一组传感器信息,我们可以通过多维格-马尔科夫进程、一个控制器的精确值来进行权衡。 美元Vtext{V_k}显示,信息估值的准确性和可量化性能,如果我们用一个不固定的计算结果来解释,那么在时间级程中,我们只能用一个不透明性数据变的状态数据函数来解释。