Online Observability of Boolean Control Networks⁎⁎This paper is funded by the Special Foundation for Basic Science and Frontier Technology Research Program of Chongqing with No.cstc2017jcyjAX0295, the Capacity Development Grant of Southwest University with No.SWU116007, the National Science Foundation of China under Grant No. 61802318 and Fundamental Research Funds for the Central Universities SWU118014

Observabililty is an important topic of Boolean control networks (BCNs). In this paper, we propose a new type of observability named online observability to present the sufficient and necessary condition of determining the initial states of BCNs, when their initial states cannot be reset. And we design an algorithm to decide whether a BCN has the online observability. Moreover, we prove that a BCN is identifiable iff it satisfies controllability and the online observability, which reveals the essence of identification problem of BCNs.