An Algorithm to Maintain the Performance of the Cyber-Physical System via Online Indicator of Operational Reliability

On-line (operational) reliability analysis and recovery process of cyber-physical systems (CPS) is under consideration. The approach is based on the division of the life- cycle into time slices with reference to the pre-emergency, emergency, restored and predicted states. Working capability restoration of the CPS is executed with respect to extremely critical and critical equipment. Constructed state graphs of the cybernetic component and the physical component are introduced. Designed differential equations link the probability of return to a working state with intensities of failures and various types restorations. Under the known initial conditions of the probabilities for corresponding states the solution of appropriate ordinary differential equations allows a clear graphical interpretation in the time domain, which shows the changes in the probability of the system components transition from one state to another by time slices of the CPS life-cycle. The developed diagram of decision-making on restoration or replacement of the corresponding component allows to make the reasonable choice of the actions option aimed on working capability restoration. An algorithm for the method implementation is developed and tested via execution of the numerical example related with Automated Parking system as a typical representative of the CPS-systems variety.