Filtering for Nonlinear Genetic Regulatory Networks With Stochastic Disturbances

Abstract

Exponential stability analysis for discrete-time switched linear systems with time-delay," Int. J. Innov. Comput., Inform. Control, vol. 3, no. 6, pp. 1557-1564 [7] L. Zhang, P. Shi, and E. Boukas, " H output-feedback control for switched linear discrete-time systems with time-varying delays," Int. J. Control, vol. 80, no. 8, pp. 1354Control, vol. 80, no. 8, pp. -1365Control, vol. 80, no. 8, pp. , 2007 [8] W. P. Dayawansa and C. F. Martin, "A converse Lyapunov theorem for a class of dynamical systems which undergo switching," IEEE Trans. Automat. Control, vol. 44, no. 4, pp. 751-760, Apr. 1999 Control, vol. 43, no. 4, pp. 555-559, Apr. 1998. [11] J. Geromel and P. Colaneri, "Stability and stabilization of discrete time switched systems," Int. J. Control, vol. 79, no. 7, pp. 719-728, 2006 [28] H. Gao, J. Lam, C. Wang, and S. Xu, " H model reduciton for discrete time-delay systems: Delay-independent and dependent approaches," Int. J. Control, vol. 77, no. 4, pp. 321-335, 2004.[29] S. Xu and J. Lam, " H model reduction for discrete-time singular systems," Syst. Control Lett., vol. 48, pp. 121-133, 2002.[30] C. Gong and B. Su, "Robust L 0 L filtering of convex polyhedral uncertain time-delay fuzzy systems," Int. J. Innov. Comput., Inform. Control, vol. 4, no. 4, pp. 793-802, 2008.[31] L. Zhang, P. Shi, E. Boukas, and C. Wang, "Robust l 0 l filtering for switched linear discrete time-delay systems with polytopic uncertainties," IET Control Theory Appl., vol. Automatica, vol. 37, no. 2, pp. 221-229, 2001. Filtering for Nonlinear Genetic Regulatory Networks With Stochastic DisturbancesZidong Wang, James Lam, Guoliang Wei, Karl Fraser, and Xiaohui LiuAbstract-In this paper, the filtering problem is investigated for nonlinear genetic regulatory networks with stochastic disturbances and time delays, where the nonlinear function describing the feedback regulation is assumed to satisfy the sector condition, the stochastic perturbation is in the form of a scalar Brownian motion, and the time delays exist in both the translation process and the feedback regulation process. The purpose of the addressed filtering problem is to estimate the true concentrations of the mRNA and protein. Specifically, we are interested in designing a linear filter such that, in the presence of time delays, stochastic disturbances as well as sector nonlinearities, the filtering dynamics of state estimation for the stochastic genetic regulatory network is exponentially mean square stable with a prescribed decay rate lower bound . By using the linear matrix inequality (LMI) technique, sufficient conditions are first derived for ensuring the desired filtering performance for the gene regulatory model, and the filter gain is then characterized in terms of the solution to an LMI, which can be easily solved by using standard software packages. A simulation example is exploited in order to illustrate the effectiveness of the proposed design procedures.

Parameters identification of unknown delayed genetic regulatory networks by a switching particle swarm optimization algorithm

“…Genetic regulatory networks (GRNs) have been extensively studied in the biological and biomedical sciences, and a large amount of results have been published over the past decade [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. Recently, GRNs with time-delays in the form of differential equations have received particular research attention [2,[8][9][10][11][12][13][14][15][16][17].…”

“…Recently, GRNs with time-delays in the form of differential equations have received particular research attention [2,[8][9][10][11][12][13][14][15][16][17]. It has been revealed that time-delays play a very important role in dynamical modelling of genetic networks, and mathematical models without introducing the delay effects may even provide wrong predictions of the mRNA and protein concentrations [5,6,8].…”

“…On the other hand, when modeling complex networks [15,16] including GRNs, the stochastic disturbances in real-world gene expression data is of great significance. The stochastic noise arises in gene expression in one of two ways, i.e., internal noise and external noise [4,10,12,14]. Moreover, it is also shown that many biological networks are complex networks with small-world and scale-free properties [7].…”

“…Moreover, it is also shown that many biological networks are complex networks with small-world and scale-free properties [7]. It is remarkable that the filtering and stability analysis issues have been addressed in [8][9][10][11][12][13][14][15][16][17] for stochastic and/or delayed GRNs delayed GRNs have been addressed [8][9][10][11][12][13][14][15][16][17].…”

“…Thus, the study of identifying the biological systems from the available data has comes in place. In [12], the authors dealt with filtering problem for estimating the states of stochastic delayed GRNs. In [17], an adaptive filtering problem of identifying unknown parameters of GRN was investigated.…”