Passive-active fault detection of Boolean control networks

Abstract

This paper investigates the fault detectability of Boolean control networks. To deal with different circumstances, passive fault detectability and four types of active fault detectability are proposed for the first time. For passive fault detectability, in line with observed input-output data, several discriminant conditions are put forward. For active fault detectability, by resorting to an auxiliary system, the essence of active fault detectabilty is revealed via reachability. Subsequently, corresponding to different types of active fault detectability, algebraic criteria that facilitate verification are provided. At the same time, the relationships of four types of active fault detectability are discussed as well. In addition, an approach for calculating fault detection time is given by combining passive fault detectability with active fault detectability. Finally, the effectiveness of the results obtained is elaborated by several examples.