Observability Verification System Analysis for Observability and Reconstructibility of Probabilistic Logical Control Networks

Observability and reconstructibility are two fundamental issues in modern control theory, which are important in both state estimation and observer design. The existing results for verifying the observability and reconstructibility of probabilistic logical control networks (PLCNs) have exponential complexities. This article presents a new approach to verify the observability and reconstructibility of PLCNs, which can greatly reduce the computational complexity. Specifically, the problem is tackled in three different steps. Firstly, based on the division of the state pair space, an observability verification system is established. Secondly, the equivalence between the stabilization of the proposed observability verification system and the observability of PLCNs is revealed, and a new criterion is established to solve the observability of PLCNs. Under the framework, the computational complexity is discussed. Thirdly, the relationship between observability and reconstructibility of PLCNs is unveiled, and some new criteria are established to solve two kinds of reconstructibility problems for PLCNs. Finally, an example of a biological network, apoptosis network, is presented to demonstrate the feasibility of the methods proposed in this article.