Observability of Boolean control networks

Abstract

Serval existing definitions for observability of Boolean control networks (BCNs) are revisited and a new definition termed observability via output feedback is proposed. This definition restricts the input sequences used to distinguish distinct initial states to be generated by output feedbacks. A technique called parallel extension is proposed for observability analysis, the main idea of which is to interconnect a BCN with its duplication in parallel and transfer the observability problem of the original BCN to the set reachability problem of the interconnected BCN. Novel necessary and sufficient conditions for observability and observability under arbitrary inputs have been given, respectively. In addition, by restricting the output feedback to be static, a sufficient condition for observability via output feedback is proposed. An example is given to illustrate the main results.