State estimation results for genetic regulatory networks with Lévy-type noise. (English) Zbl 07848593
Summary: In this paper, we investigate some novel results on \(H_\infty\) state estimation for genetic regulatory networks (GRNs) with time-varying delays and Lévy-type noise. The objective of present study is to design the estimator for the considered GRN to analyze the concentrations of mRNAs and proteins through the measured available outputs. The sufficient conditions for stochastic stability of error system is derived by constructing an appropriate Lyapunov-Krasovskii functional (LKF) together with a free-weighing matrix technique and Kunita’s estimate. Further, the results are extended to study \(H_\infty\) state estimation results. Finally, a physical example of transcriptional regulator is considered to show the effectiveness and feasibility of the proposed estimation scheme.
MSC:
| 92Cxx | Physiological, cellular and medical topics |
| 93Dxx | Stability of control systems |
| 93Exx | Stochastic systems and control |
Keywords:
genetic regulatory network; Lévy noise; state estimation; Poisson process; time-varying delaysReferences:
| [1] | Alberts, B.; Bray, D.; Hopkin, K.; Johnson, A.; Lewis, J.; Raff, M.; Roberts, K.; Walter, P., Essential cell biology, 2000, Garland Science: Garland Science New York |
| [2] | Li, C.; Chen, L.; Aihara, K., Stability of genetic networks with SUM regulatory logic: Lur’s systems and LMI approach, IEEE. T. Circuits-I, 53, 2451-2458, 2006 · Zbl 1374.92045 |
| [3] | Oksendal, B., Stochastic Differential Equations, 5th edition, 2003, Springer-Verlag: Springer-Verlag NewYork · Zbl 1025.60026 |
| [4] | Ali, M. S.; Agalya, R.; Hong, K. S., Non-fragile synchronization of genetic regulatory networks with randomly occurring controller gain fluctuation, Chin. J. Phys., 62, 132-143, 2019 · Zbl 07828444 |
| [5] | Zou, C.; Wang, X., Robust stability of delayed Markovian switching genetic regulatory networks with reaction-diffusion terms, Comput. Math. Appl., 79, 1150-1164, 2020 · Zbl 1448.92086 |
| [6] | Lai, Q., Stability and bifurcation of delayed bidirectional gene regulatory networks with negative feedback loops, Chin. J. Phys., 56, 1064-1073, 2018 · Zbl 07819493 |
| [7] | Liu, C.; Wang, X.; Xue, Y., Global exponential stability analysis of discrete-time genetic regulatory networks with time-varying discrete delays and unbounded distributed delays, Neurocomput., 372, 100-108, 2020 |
| [8] | Smolen, P.; Baxter, D. A.; Byrne, J. H., Mathematical modeling of gene networks review, Neuron, 26, 567-580, 2000 |
| [9] | Wang, Z.; Gao, H., Dynamics analysis of gene regulatory networks, Int. J. Syst. Sci., 41, 1-4, 2010 · Zbl 1298.00190 |
| [10] | Ribeiro, A. S., Kinetics of gene expression in bacteria - from models to measurements and back again, Can. J. Chem., 91, 487-494, 2013 |
| [11] | Han, Y.; Zhang, X.; Wang, Y., Asymptotic stability criteria for genetic regulatory networks with time-varying delays and reaction-diffusion terms, Circ. Syst. Signal PR., 34, 3161-3190, 2015 · Zbl 1341.93070 |
| [12] | Dong, Y.; Chen, L.; Mei, S., Observer design for neutral-type neural networks with discrete and distributed time-varying delays, Int. J. Adapt. Control., 2019 · Zbl 1417.93263 |
| [13] | Anbuvithya, R.; Mathiyalagan, K.; Sakthivel, R.; Prakash, P., Sampled-data state estimation for genetic regulatory networks with time-varying delays, Neurocomput., 151, 737-744, 2015 |
| [14] | Liu, Y.; Wang, Z.; Liu, X., State estimation for discrete-time Markovian jumping neural networks with mixed mode dependent delays, Phys. Lett. A., 372, 7147-7155, 2008 · Zbl 1227.92002 |
| [15] | Bao, H.; Cao, J., Delay distribution dependent state estimation for discrete-time stochastic neural networks with random delay, Neural Netw., 24, 19-28, 2011 · Zbl 1222.93213 |
| [16] | Zhang, X.; Han, Y.; Wu, L.; Wang, Y., State estimation for delayed genetic regulatory networks with reaction - diffusion terms, IEEE. T. Neur. Net. Lear., 29, 299-309, 2018 |
| [17] | Liang, J.; Lam, J., Robust state estimation for stochastic genetic regulatory networks, Int. J. Syst. Sci., 41, 47-63, 2010 · Zbl 1291.93298 |
| [18] | Ali, M. S.; Saravanan, S.; Palanisamy, L., Stochastic finite-time stability of reaction diffusion Cohen-Grossberg neural networks with time-varying delays, Chin. J. Phys., 57, 314-328, 2019 · Zbl 1539.93190 |
| [19] | Lee, T. H.; Lakshmanan, S.; Park, J. H.; Balasubramaniam, P., State estimation for genetic regulatory networks with mode dependent leakage delays, time-varying delays and markovian jumping parameters, IEEE. T. Nanobiosci., 12, 363-375, 2013 |
| [20] | Duan, Q.; Su, H.; Wu, Z., H_∞state estimation of static neural networks with time-varying delay, Neurocomput., 97, 16-21, 2012 |
| [21] | Wang, T.; Ding, Y.; Zhang, L.; Hao, K., Robust state estimation for discrete-time stochastic genetic regulatory networks with probabilistic measurement delays, Neurocomput., 111, 1-12, 2013 |
| [22] | Sheng, S.; Zhang, X.; Lu, Q.; Lu, G., Event-triggered H_∞ state estimation for coupled and switched genetic regulatory networks, Circ. Syst. Signal. PR., 38, 4420-4445, 2019 |
| [23] | Jiao, T.; Zheng, W. X.; Xu, S., On stability of a class of switched nonlinear systems subject to random disturbances, IEEE. T. Circuits-I., 63, 2278-2289, 2016 |
| [24] | Jiao, T.; Zong, G.; Nguang, S. K.; Zhang, C., Stability analysis of genetic regulatory networks with general random disturbances, IEEE. T. Nanobiosci., 18, 128-135, 2018 |
| [25] | Shen, H.; Men, Y.; Cao, J.; Park, J. H., H_∞ filtering for fuzzy jumping genetic regulatory networks with round robin protocol: a hidden markov model based approach, IEEE. T. Fuzzy. Syst., 28, 112-121, 2020 |
| [26] | Huang, G.-R.; Saakian, D. B.; Hu, C. K., Accurate analytic solution of chemical master equations for gene regulation networks in a single cell, Phys. Rev. E., 97, 012412, 2018 |
| [27] | Hung, Y. C.; Hu, C. K., Constructive role of noise in p53 regulatory network, Comput. Phys. Commun., 182, 249-250, 2011 · Zbl 1216.92038 |
| [28] | P07019 · Zbl 1456.92061 |
| [29] | Zhu, Q., Asymptotic stability in the pth moment for stochastic differential equations with lévy noise, J. Math. Anal. Appl., 416, 126-142, 2014 · Zbl 1309.60065 |
| [30] | Kunita, H., Stochastic differential equations based on Lévy processes and stochastic flows of diffeomorphisms, 2004, Real and Stochastic Analysis, Trends in Mathematics. Birkhäuser Boston · Zbl 1082.60052 |
| [31] | Applebaum, D., Lévy Process and Stochastic Calculus, 2009, Cambridge University Press · Zbl 1200.60001 |
| [32] | Applebaum, D.; Siakalli, M., Stochastic stabilization of dynamical systems using lévy noise, Stochastic Dyn., 10, 509-527, 2010 · Zbl 1218.93106 |
| [33] | Wu, F.; Chen, X.; Zheng, Y.; Duan, J.; Kurths, J.; Li, X., Lévy noise induced transition and enhanced stability in a gene regulatory network, Chaos, 28, 075510, 2018 · Zbl 1396.92026 |
| [34] | Luo, Q.; Gong, Y.; Jia, C., Stability of gene regulatory networks with Lévy noise, Sci. China. Inform. Sci., 60, 072264, 2017 |
| [35] | Long, H.; Ma, C.; Shimizu, Y., Least squares estimators for stochastic differential equations driven by small Lévy noises, Stoch. Proc. Appl., 127, 1475-1495, 2017 · Zbl 1362.62048 |
| [36] | Zhu, X. Q., Stability of stochastic differential equations with lévy noise, Proc. 33rd Chinese Control Conf., Nanjing, 5211-5216, 2014 |
| [37] | Zheng, Y.; Serdukova, L.; Duan, J.; Kurths, J., Transitions in a genetic transcriptional regulatory system under Lévy motion, Sci. Rep., 6, 29274, 2016 |
| [38] | Chen, X.; Wu, F.; Duan, J.; Kurths, J.; Li, X., Most probable dynamics of a genetic regulatory network under stable Lévy noise, Appl. Math. Comput., 348, 425-436, 2019 · Zbl 1428.92036 |
| [39] | Chen, W.; Chen, D.; Hu, J.; Liang, J.; Dobaie, A. M., A sampled-data approach to robust H_∞ state estimation for genetic regulatory networks with random delays, Int. J. Control. Autom., 16, 491-504, 2018 |
| [40] | Liu, A.; Yu, L.; Zhang, D.; Zhang, W., Finite-time H_∞ control for discrete-time genetic regulatory networks with random delays and partly unknown transition probabilities, J. Franklin Inst., 350, 1944-1961, 2013 · Zbl 1392.93051 |
| [41] | Feng, Z.; Lam, J., Integral partitioning approach to robust stabilization for uncertain distributed time-delay systems, Int. J. Robust Nonlin., 22, 676-689, 2012 · Zbl 1273.93140 |
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