On Synchronization Design and State Observer Design of (Singular) Boolean Networks

• Published in: IEEE transactions on circuits and systems. I, Regular papers Vol. 70; no. 12; pp. 5456 - 5467
• Main Authors: Sun, Liangjie, Ching, Wai-Ki, Zhu, Shiyong, Lu, Jianquan
• Format: Journal Article
• Language: English
• Published: New York IEEE 01-12-2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Biological system modeling; Boolean; Boolean functions; Boolean networks; Design; Mathematical models; matrix equation; Observers; singular Boolean networks; State estimation; state observer; State observers; Synchronism; Synchronization; Trajectory
• ISSN: 1549-8328; 1558-0806
• DOI: 10.1109/TCSI.2023.3316456

This paper first investigates the synchronization design problem for both Boolean networks (BNs) and singular BNs. According to the complete family of reachable sets, all possible synchronized response BNs and all possible weakly synchronized response singular BNs can be constructed. Subsequently, it is noted that there is similarity between synchronized response (singular) BNs and state observers. The synchronized response (singular) BN is constructed based on the state of a given drive (singular) BN, making its state gradually tend to be consistent with the state of the given drive (singular) BN. While the state observer is designed based on the output of a given real (singular) BN, making its state (state estimation) gradually tend to be consistent with the state of the given real (singular) BN. Therefore, consider applying the results for constructing synchronized response (singular) BNs to designing state observers for (singular) BNs. Specifically, the real (singular) BN to be observed can be regarded as a drive (singular) BN. Consequently, the problem for designing state observers can be transformed into the problem for constructing response (singular) BNs that achieve synchronization with a given real (singular) BN, and then the gain matrix of the designed state observer can be obtained by solving a matrix equation. The method for designing state observers is superior to other methods in that the accurate estimated time for designed state observers can be determined and adjusted to some certain extent, and all possible state observers in the considered form can be designed.