Minimum-Time and Minimum-Triggering Observability of Stochastic Boolean Networks

• Published in: IEEE transactions on automatic control Vol. 67; no. 3; pp. 1558 - 1565
• Main Authors: Zhu, Shiyong, Lu, Jianquan, Lin, Lin, Liu, Yang
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.03.2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algebraic state space representation (ASSR) approach; Asymptotic stability; Boolean; Boolean algebra; Boolean functions; Linear programming; Markovian jump Boolean networks (MJBNs); Maximum principle; minimum-time control; minimum-triggering control; Numerical stability; Observability; Observability (systems); Output feedback; Stability criteria; State space models; Switches; Two dimensional displays
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2021.3069739

This article investigates the observability of Markovian jump Boolean networks (MJBNs) via algebraic state space representation approach. A necessary and sufficient criterion in the form of linear programming is derived for the asymptotic observability in distribution of MJBNs, and several conditions are obtained for the finite-time observability based on the properties of nilpotent matrices. Subsequently, in order to minimize the time consumption, a maximum principle is established to address the minimum-time observability problem. With regard to the event-triggered output feedback observability, an efficient procedure is developed to minimize the number of triggering events. Finally, three numerical examples are employed to demonstrate the effectiveness of theoretical results.