Detectability of Boolean networks: A finite-time convergent matrix approach

Abstract

This paper investigates the detectability of Boolean networks (including Boolean control networks (BCNs) and probabilistic Boolean networks (PBNs)) and reveals the relationship between detectability and observability from the perspective of decompositions. Firstly, the single-experiment detectability and the arbitrary-experiment detectability of BCNs are converted into the consistent reachability and the any-input sequence reachability of a logica control network through an augmented approach. Then these two kinds of detectability are testified via two defined non-augmented matrix sequences. Moreover, some algorithms are given to obtain the current state and suitable input sequences satisfying corresponding detectability. Subsequently, the non-augmented approach is used to discuss the strong detectability of PBNs, and is generalized to analyze detectability and observability decompositions of BCNs. Finally, several examples are presented to illustrate these results.