Under What Conditions Does a Digital Shadow Track a Periodic Linear Physical System?

The synchronization between a Digital Shadow (DS) and a Cyber-Physical System (CPS) is paramount to enable anomaly detection, predictive maintenance, what-if analysis, etc. Such synchronization means that a simulation reflects, as closely as possible, the states of the CPS. The simulation however, requires the complete initial state of the system to be known, which is often infeasible in real applications. In our work, we study the conditions under which knowing the initial state of the system is irrelevant for a simulation to eventually synchronize with the CPS. We apply traditional stability analysis to answer this question for linear periodic systems. We demonstrate the method using a simple but representative system, an incubator with a periodic control signal.

Automated summary

The complete initial state of a system is not always necessary for synchronization between a Digital Shadow and a Cyber-Physical System. Traditional stability analysis can determine the conditions under which a simulation can eventually synchronize with the CPS even without knowing the initial state.