We consider the problem of remotely tracking the state of and unstable linear time-invariant plant by means of data transmitted through a noisy communication channel from an algorithmic point of view. Assuming the dynamics of the plant are known, does there exist an algorithm that accepts a description of the channel's characteristics as input, and returns 'Yes' if the transmission capabilities permit the remote tracking of the plant's state, 'No' otherwise? Does there exist an algorithm that, in case of a positive answer, computes a suitable encoder/decoder-pair for the channel? Questions of this kind are becoming increasingly important with regards to future communication technologies that aim to solve control engineering tasks in a distributed manner. In particular, they play an essential role in digital twinning, an emerging information processing approach originally considered in the context of Industry 4.0. Yet, the abovementioned questions have been answered in the negative with respect to algorithms that can be implemented on idealized digital hardware, i.e., Turing machines. In this article, we investigate the remote state estimation problem in view of the Blum-Shub-Smale computability framework. In the broadest sense, the latter can be interpreted as a model for idealized analog computation. Especially in the context of neuromorphic computing, analog hardware has experienced a revival in the past view years. Hence, the contribution of this work may serve as a motivation for a theory of neuromorphic twins as a counterpart to digital twins for analog hardware.
翻译:我们从算法的角度来考虑通过一个吵闹的通信渠道传输数据来远程跟踪该厂的状况和不稳定线性时变工厂的问题。假设该厂的动态是已知的,那么是否存在着一种算法,接受对该频道特性的描述作为投入,如果传输能力允许远程跟踪该厂状态,“否”就返回“是 ”?是否存在一种算法,如果得到肯定的答复,可以计算出该频道的适当编码器/脱coder-pair?这类问题对于未来旨在以分布方式解决控制工程任务的通信技术来说越来越重要。特别是,在数字配对中,一种新兴的信息处理方法在最初在工业4.0背景下考虑的正在形成。然而,上述问题的答案是否定的,这种算法可以在理想化数字化数字硬件(即涡轮机)上实施。在这个文章中,我们从Blum-Shub-Smal-Scomlial可变性的模型的角度来研究远程状态估算问题,对于旨在以分布式方式解决工程任务的未来通信技术问题来说,问题越来越重要。在数字配对数字性结配对模型进行解释时,在后一个具有广义的机变的机变的机变的机变的机变的理论中,可以解释一个具有历史的机变的机变的机变的机变的机变的机变的机变的机变的机变的机变的机变。在后变的机变的机变的机变的机变的机变的机变的机变。