A survey on observability of Boolean control networks

Abstract Observability is a fundamental property of partially observed dynamical system, which means whether one can use an input sequence and the corresponding output to determine initial state. provides bases for many related problems, such as state estimation, identification, disturbance decoupling, controller synthesis, etc. Until now, improvement has been obtained in observability Boolean control networks (BCNs) mainly based on two methods—Edward F. Moore’s partition our graph (or their equivalent representations found later semitensor product (STP) matrices (where STP was proposed by Daizhan Cheng)), including necessary sufficient conditions different types observability, extensions probabilistic (PBNs) singular BCNs, even nondeterministic finite-transition systems (NFTSs); development (with help matrices) topics, computation smallest invariant dual subspaces BNs containing set functions, multiple-experiment verification/decomposition decoupling This paper thorough survey these topics. The contents are guided above methods. First, we show that partition-based method closely relates following problems: BNs, BCNs. However, this does not apply other or systems. Second, graph, four have verified verification results also extended PBNs, NFTSs. In addition, shows similarities between BCNs linear time-invariant (LTI) systems, e.g., functions vs unobservable LTI forms quotient decomposition both there essential differences “all plausible definitions turn out be equivalent” (by Walter M. Wonham 1985), but exist nonequivalent BCNs; system always exists while BCN.