Variance-constrained filtering for discrete-time genetic regulatory networks with state delay and random measurement delay

ABSTRACT

This paper is concerned with the variance-constrained filtering problem for a class of discrete-time genetic regulatory networks (GRNs) with state delay and random one-step measurement delay. The phenomenon of the random one-step measurement delay is characterised by a random variable, which is assumed to obey the Bernoulli distribution with known occurrence probability. The purpose of the addressed problem is to design a filter such that, in the presence of state delay and random one-step measurement delay, an upper bound of the filtering error covariance matrix can be obtained and the explicit expression of the filter gain matrix is given. Then, the proposed variance-constrained filtering method can be used to approximate the concentrations of mRNAs and proteins. Finally, a numerical example is provided to illustrate the effectiveness of the designed filtering scheme.

KEYWORDS:

• Genetic regulatory networks
• variance-constrained filter
• state delay
• random one-step measurement delay

Acknowledgments

The authors would like to express appreciation to the anonymous reviewers and Editors for their very helpful comments that improved the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Jun Hu  http://orcid.org/0000-0002-7852-5064

Additional information

Funding

This paper is supported by the National Natural Science Foundation of China [grant number 11301118], [grant number 61503001]; the Fok Ying Tung Education Foundation of China [grant number 151004]; the Natural Science Foundation of Heilongjiang Province of China [grant number A2018007]; the Outstanding Youth Science Foundation of Heilongjiang Province of China [grant number JC2018001]; the University Nursing Program for Young Scholars with Creative Talents in Heilongjiang Province of China [grant number UNPYSCT-2016029]; the Science Funds for the Young Innovative Talents of HUST of China [grant number 201508].

Notes on contributors

Dongyan Chen

Dongyan Chen received the B.Sc. degree in Department of Mathematics from Northeast Normal University, Changchun, China, in 1985, M.Sc. degree in Operational Research from Jilin University, Changchun, China, in 1988, and the Ph.D. degree in Aerocraft Design from Harbin Institute of Technology, Harbin, China, in 2000. She is now a Professor and PhD Supervisor with the Department of Applied Mathematics, Harbin University of Science and Technology, Harbin, China. Her current research interests include robust control, time-delay systems, optimisation approach, system optimisation and supply chain management.

Weilu Chen

Weilu Chen received the B.Sc. degree in Information and Computing Science from Harbin University of Science and Technology, Harbin, China, in 2015. She is now working toward the M.Sc. degree in Operational Research and Control Theory with the Department of Applied Mathematics, Harbin University of Science and Technology, Harbin, China. Her current research interests include robust control, time-delay systems and genetic regulatory networks.

Jun Hu

Jun Hu received the B.Sc. degree in Information and Computation Science and M.Sc. degree in Applied Mathematics from Harbin University of Science and Technology, Harbin, China, in 2006 and 2009, respectively, and the Ph.D. degree in Control Science and Engineering from Harbin Institute of Technology, Harbin, China, in 2013. From September 2010 to September 2012, he was a Visiting Ph.D. Student in the Department of Information Systems and Computing, Brunel University, U.K. From May 2014 to April 2016, he was an Alexander von Humboldt research fellow at the University of Kaiserslautern, Kaiserslautern, Germany. His research interests include nonlinear control, filtering and fault estimation, time-varying systems and complex networks. He has published more than 30 papers in refereed international journals. He serves as a reviewer for Mathematical Reviews, as an editor for IEEE Access, Neurocomputing, Journal of Intelligent and Fuzzy Systems, Neural Processing Letters, Systems Science and Control Engineering, and as a guest editor for International Journal of General Systems and Information Fusion.

Hongjian Liu

Hongjian Liu received the B.Sc. degree in Applied Mathematics in 2003 from Anhui University, Hefei, China and the M.Sc. degree in Detection Technology and Automation Equipments in 2009 from Anhui Polytechnic University, Wuhu, China, and the Ph.D. degree in Control Theory and Control Engineering in 2018 from Donghua University, Shanghai, China. He is currently an Associate Professor in the School of Mathematics and Physics, Anhui Polytechnic University, Wuhu, China. His current research interests include filtering theory, memristive neural networks and network communication systems. He is a very active reviewer for many international journals.