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Minimum observability of probabilistic Boolean networks

Authors :
Xu, Jiayi
Fu, Shihua
Xia, Liyuan
Wang, Jianjun
Publication Year :
2024

Abstract

This paper studies the minimum observability of probabilistic Boolean networks (PBNs), the main objective of which is to add the fewest measurements to make an unobservable PBN become observable. First of all, the algebraic form of a PBN is established with the help of semi-tensor product (STP) of matrices. By combining the algebraic forms of two identical PBNs into a parallel system, a method to search the states that need to be H-distinguishable is proposed based on the robust set reachability technique. Secondly, a necessary and sufficient condition is given to find the minimum measurements such that a given set can be H-distinguishable. Moreover, by comparing the numbers of measurements for all the feasible H-distinguishable state sets, the least measurements that make the system observable are gained. Finally, an example is given to verify the validity of the obtained results.

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.2401.12468
Document Type :
Working Paper