Feedback control design for the complete synchronisation of two coupled Boolean networks

Abstract

In the literatures, to design state feedback controllers to make the response Boolean network synchronise with the drive Boolean network is rarely considered. Motivated by this, feedback control design for the complete synchronisation of two coupled Boolean networks is investigated in this paper. A necessary condition for the existence of a state feedback controller achieving the complete synchronisation is established first. Then, based on the necessary condition, the feedback control law is proposed. Finally, an example is worked out to illustrate the proposed design procedure.

Keywords:

• Boolean network
• synchronisation
• feedback control design
• semi-tensor product

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant numbers 61403139, 11371137]; Science and Technology Commission of Shanghai Municipality [grant number 14YF1404500]; Fundamental Research Funds for the Central Universities [grant number 222201314009].

Notes on contributors

Fangfei Li

Fangfei Li received her BS degree from Liaoning Normal University in Dalian, in 2004, MS degree from University of Shanghai for Science and Technology in Shanghai, in 2007 and PhD degree from Tongji University in Shanghai, in 2012. Since 2012 she is serving as a lecturer at the Department of Mathematics, East China University of Science and Technology in Shanghai. Her research interests include Boolean networks, impulsive hybrid systems, systems biology etc.