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A Sampled-data Approach to Robust H∞ State Estimation for Genetic Regulatory Networks with Random Delays

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  • Control Theory and Applications
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Abstract

This paper is concerned with the robust H∞ state estimation problem for a class of uncertain genetic regulatory networks (GRNs) with random delays and external disturbances by using sample-data method. An important feature of this paper is that the time-varying delays are assumed to be random and their probability distributions are known a priori. By substituting the continuous measurements, the sampled measurements are used to estimate the concentrations of mRNAs and proteins. On the basis of the extended Wirtinger inequality, a discontinuous Lyapunov functional is introduced. Then, some sufficient conditions are derived in terms of a set of linear matrix inequalities (LMIs), which ensure that the error system is globally asymptotically stable in the meansquare sense and satisfies H∞ performance. Further, the explicit expression of the required estimator gain matrices is proposed. Finally, a numerical example is used to illustrate the effectiveness and feasibility of the obtained estimation method.

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Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Harbin University of Science and Technology, Harbin, 150080, China

    Weilu Chen, Dongyan Chen & Jun Hu

  2. School of Mathematics, Southeast University, Nanjing, 210096, China

    Jinling Liang

  3. Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Abdullah M. Dobaie

Authors
  1. Weilu Chen
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  2. Dongyan Chen
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  3. Jun Hu
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  4. Jinling Liang
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  5. Abdullah M. Dobaie
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Corresponding authors

Correspondence to Dongyan Chen or Jun Hu.

Additional information

Recommended by Associate Editor Yang Tang under the direction of Editor Hamid Reza Karimi. This work was supported by the National Natural Science Foundation of China (61673141, 61673110, 11271103, 11301118), the Fok Ying Tung Education Foundation of China (151004), the University Nursing Program for Young Scholars with Creative Talents in Heilongjiang Province under Grant UNPYSCT-2016029, the Science Funds for the Young Innovative Talents of HUST, the Postdoctoral Scientific Research Developmental Found of Heilongjiang Province of China under Grant LBH-Q16120, and the Alexander von Humboldt Foundation of Germany.

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.

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, optimization approach, system optimization and supply chain management.

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. He is currently a Professor with the Department of Applied Mathematics, Harbin University of Science and Technology, Harbin, China. His current research interests include nonlinear control, filtering and fault estimation, time-varying systems, multi-agent systems and complex networks. He has published more than 20 papers in refereed international journals. He serves as a reviewer for Mathematical Reviews, as an editor for Neurocomputing, Journal of Intelligent & Fuzzy Systems, Neural Processing Letters, Systems Science & Control Engineering, and as a guest editor for International Journal of General Systems and Information Fusion. He is an active reviewer for many international journals.

Jinling Liang received the BSc and MSc degrees in mathematics from Northwest University, Xi’an, China, in 1997 and 1999, respectively, and the PhD degree in applied mathematics from Southeast University, Nanjing, China, in 2006. She is currently a professor in the Department of Mathematics, Southeast University. She has published around 80 papers in refereed international journals. Her current research interests include complex networks, non-linear systems and bioinformatics. She serves as an associate editor for several international journals such as the IEEE Transactions on Neural Networks and Learning Systems, the IET Control Theory & Applications, and the International Journal of Computer Mathematics.

Abdullah M. Dobaie received his B.Sc. degree in 1981 and M.Sc. degree in 1989, both in Electronic and Communication Engineering from King Abdulaziz University in Saudi Arabia, and the Ph.D. degree in 1995 from Colorado State University in USA. He is the supervisor of many masters in science and has directed many projects concerning communication, digital filters, antenna and digital signal processing. His recent interests include adaptive communication systems, digital image processing, wave propagation and communication networks.

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Chen, W., Chen, D., Hu, J. et al. A Sampled-data Approach to Robust H∞ State Estimation for Genetic Regulatory Networks with Random Delays. Int. J. Control Autom. Syst. 16, 491–504 (2018). https://doi.org/10.1007/s12555-017-0106-2

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  • DOI: https://doi.org/10.1007/s12555-017-0106-2

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