Minimal finite-time observability of Markovian jump Boolean networks

Lina Wang, Zicong Xia, Yang Liu, Shun-ichi Azuma, Weihua Gui

Abstract: In this paper, the finite-time observability and minimal finite-time observability problems of Markovian jump Boolean networks (MJBNs) are addressed. The signal space is partitioned to facilitate the observability analysis, followed by novel criteria for the finite-time observability of MJBNs. To reduce measurement costs, a minimal finite-time observability problem is formulated, involving the injection of the minimum number of sensors necessary for an unobservable MJBN to achieve finite-time observability. By introducing an indicator matrix, the minimal finite-time observability problem is converted into a 0–1 programming problem, and a collaborative neurodynamic optimization approach with multiple recurrent neural networks is developed for obtaining a global optimal solution. Two illustrative examples, including a biological simulation, are provided to demonstrate the theoretical results.