3 research outputs found
Neuromorphic Twins for Networked Control and Decision-Making
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
On the Need of Analog Signals and Systems for Digital-Twin Representations
We consider the task of converting different digital descriptions of analog
bandlimited signals and systems into each other, with a rigorous application of
mathematical computability theory. Albeit very fundamental, the problem appears
in the scope of digital twinning, an emerging concept in the field of digital
processing of analog information that is regularly mentioned as one of the key
enablers for next-generation cyber-physical systems and their areas of
application. In this context, we prove that essential quantities such as the
peak-to-average power ratio and the bounded-input/bounded-output norm, which
determine the behavior of the real-world analog system, cannot generally be
determined from the system's digital twin, depending on which of the
above-mentioned descriptions is chosen. As a main result, we characterize the
algorithmic strength of Shannon's sampling type representation as digital twin
implementation and also introduce a new digital twin implementation of analog
signals and systems. We show there exist two digital descriptions, both of
which uniquely characterize a certain analog system, such that one description
can be algorithmically converted into the other, but not vice versa
Trustworthy Digital Representations of Analog Information—An Application-Guided Analysis of a Fundamental Theoretical Problem in Digital Twinning
This article compares two methods of algorithmically processing bandlimited time-continuous signals in light of the general problem of finding “suitable” representations of analog information on digital hardware. Albeit abstract, we argue that this problem is fundamental in digital twinning, a signal-processing paradigm the upcoming 6G communication-technology standard relies on heavily. Using computable analysis, we formalize a general framework of machine-readable descriptions for representing analytic objects on Turing machines. Subsequently, we apply this framework to sampling and interpolation theory, providing a thoroughly formalized method for digitally processing the information carried by bandlimited analog signals. We investigate discrete-time descriptions, which form the implicit quasi-standard in digital signal processing, and establish continuous-time descriptions that take the signal’s continuous-time behavior into account. Motivated by an exemplary application of digital twinning, we analyze a textbook model of digital communication systems accordingly. We show that technologically fundamental properties, such as a signal’s (Banach-space) norm, can be computed from continuous-time, but not from discrete-time descriptions of the signal. Given the high trustworthiness requirements within 6G, e.g., employed software must satisfy assessment criteria in a provable manner, we conclude that the problem of “trustworthy” digital representations of analog information is indeed essential to near-future information technology