Topography Relaxation in Determining Unsafe State Intersections for Uncertain CPS

Abstract

Human-in-the-loop systems are systems that consider the presence of humans, human errors, and human interactions with a system. Accurate and validated sensing, coordinated control and decision over human errors and interactions, even at a scale and complexity, should be done reliably and seamlessly. In these systems, sensors, while being discretized and processed digitally, nevertheless represent physical properties. Therefore, modeling of these very large systems faces two key challenges: 1) While computing aspects can be represented using discrete-time events, physical parameters can only be monitored adequately using continuous-time models, and 2) with human factors involved, behavior modeling is intractable and highly inaccurate. Conventional and state-of-the-art systems always limit themselves in terms of the bounded measure calculated from the data available, without factoring in human rational information verification. In this article, uncertainty theory-based cyber-physical state-space approximation is proposed. These approximations are further morphed topographically based on Ricci flow and fuzzy qualifiers to match human verification of sensor data. The results show that sensor information can be formally approximated, verified, and identified by human belief degrees. To the best of our knowledge, this is the first implementation of Ricci flow in the domain of fuzzy cyber-physical systems, and it has the potential to improve overall reachable set interpretability with qualitative and quantitative interpretation.