On detectability of Boolean control networks

Abstract

This paper introduces the detectability notions and investigates the detectability properties for Boolean networks (BNs) and Boolean control networks (BCNs). A BN (BCN) possesses the property of detectability if the current state can be determined by limited observed data. According to different situations, three types of detectabilities are defined: strong detectability, detectability and weak detectability. Firstly, using the semi-tensor product of matrices, the BCN is written as an equivalent algebraic expression, which is called the data form. Secondly, some criterion and detection algorithms are provided for checking detectabilities via this novel form. Thirdly, four types of properties: stability, stabilizability, observability and detectability, are compared and analyzed, and then their relationships are clearly described in two diagrams, which provide a new perspective to analyze the characterization of BNs and BCNs. Finally, for better presentation, two practical examples are presented to show the effectiveness of the obtained new results.