Reconstructibility Analysis and Observer Design for Boolean Control Networks

The reconstructibility analysis and observer design for general Boolean control networks (BCNs) are investigated in this paper. At first, to discriminate reconstructibility from observability, the relationship between different types of observability and reconstructibility existing in the literature is studied. For reconstructibility analysis, explicit and recursive methods are derived. A termination condition is provided to avoid the running of the recursive method longer than necessary. After that, if a general BCN is reconstructible, then an approach for observer design is given. The Luenberger-like observer for general BCNs is introduced to facilitate an online implementation. The state estimate always contains the real state and converges to the real state at a time not later than the minimal reconstructibility index. Finally, examples are given to illustrate the proposed approaches.