TY - JOUR
T1 - Remote State Estimation and Blum-Shub-Smale Machines-A Computability Analysis with Applications to Virtual-Twinning
AU - Boche, Holger
AU - Böck, Yannik
AU - Deppe, Christian
AU - Fitzek, Frank H.P.
N1 - Publisher Copyright:
© 1963-2012 IEEE.
PY - 2024
Y1 - 2024
N2 - The present article analyzes aspects of the problem of remote state estimation via noisy communication channels (RSE) for their Blum-Shub-Smale (BSS) computability, motivated by an exemplary application to a formal model of virtual twinning subject to stringent integrity requirements. Computability theory provides a unique framework for the formal and mathematically rigorous analysis of algorithms and computing machines. Therefore, computability theory is essential in the domain of safety- and life-critical technology, where the formal verification of automated systems is necessary. Based on the RSE problem, we establish a simple mathematical model of virtual-twin systems that entails a formal notion of integrity (i.e., a state where the virtual entity accurately mirrors its physical counterpart). The model's notion of integrity is related to the question of whether the system under consideration is capable of computing the communication channel's zero-error capacity and corresponding zero-error codes. While this task is known to exceed the theoretical capabilities of Turing computers, we prove its formal feasibility within the model BSS machines. As different authors have proposed BSS machines as potential model of some forms of analog computing, this article serves as a proof-of-concept for a theoretical analog supremacy of unconventional information-processing hardware. Considering recent advances in the development of such hardware, forms of analog supremacy will likely become relevant in the future of cyber-physical systems and information technology.
AB - The present article analyzes aspects of the problem of remote state estimation via noisy communication channels (RSE) for their Blum-Shub-Smale (BSS) computability, motivated by an exemplary application to a formal model of virtual twinning subject to stringent integrity requirements. Computability theory provides a unique framework for the formal and mathematically rigorous analysis of algorithms and computing machines. Therefore, computability theory is essential in the domain of safety- and life-critical technology, where the formal verification of automated systems is necessary. Based on the RSE problem, we establish a simple mathematical model of virtual-twin systems that entails a formal notion of integrity (i.e., a state where the virtual entity accurately mirrors its physical counterpart). The model's notion of integrity is related to the question of whether the system under consideration is capable of computing the communication channel's zero-error capacity and corresponding zero-error codes. While this task is known to exceed the theoretical capabilities of Turing computers, we prove its formal feasibility within the model BSS machines. As different authors have proposed BSS machines as potential model of some forms of analog computing, this article serves as a proof-of-concept for a theoretical analog supremacy of unconventional information-processing hardware. Considering recent advances in the development of such hardware, forms of analog supremacy will likely become relevant in the future of cyber-physical systems and information technology.
KW - Autonomous systems
KW - control over communications
KW - fault detection
KW - neuromorphic computing
UR - http://www.scopus.com/inward/record.url?scp=85210117652&partnerID=8YFLogxK
U2 - 10.1109/TAC.2024.3502314
DO - 10.1109/TAC.2024.3502314
M3 - Article
AN - SCOPUS:85210117652
SN - 0018-9286
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
ER -