Robust filtering for gene expression time series data with variance constraints
Robust filtering for gene expression time series data with variance constraints
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DOI：
10.1080/00207160601134433
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发表时间：
2007-05
影响因子：
1.8
通讯作者：
G. Wei;Zidong Wang;H. Shu;K. Fraser;Xiaohui Liu
中科院分区：
文献类型：
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作者：
G. Wei;Zidong Wang;H. Shu;K. Fraser;Xiaohui Liu
在本文中，采用不确定离散时间随机系统来表示时间序列数据的基因调控网络模型。研究了具有随机扰动和范数有界参数不确定性的基因表达模型的鲁棒方差约束滤波问题，其中随机扰动采用具有恒定方差的标量高斯白噪声的形式，并且参数不确定性同时进入系统矩阵和输出矩阵。所解决的鲁棒滤波问题的目的是设计一个线性滤波器，使得对于允许的有界不确定性，滤波误差系统是Schur稳定的并且个体误差方差小于预先指定的上限。通过使用线性矩阵不等式（LMI）技术，首先导出充分条件以确保基因表达模型达到所需的过滤性能。然后滤波器增益用一组 LMI 的解来表征，这可以通过使用可用的软件包轻松解决。利用基因表达模型的模拟示例来证明所提出的设计程序的有效性。
In this paper, an uncertain discrete-time stochastic system is employed to represent a model for gene regulatory networks from time series data. A robust variance-constrained filtering problem is investigated for a gene expression model with stochastic disturbances and norm-bounded parameter uncertainties, where the stochastic perturbation is in the form of a scalar Gaussian white noise with constant variance and the parameter uncertainties enter both the system matrix and the output matrix. The purpose of the addressed robust filtering problem is to design a linear filter such that, for the admissible bounded uncertainties, the filtering error system is Schur stable and the individual error variance is less than a prespecified upper bound. By using the linear matrix inequality (LMI) technique, sufficient conditions are first derived for ensuring the desired filtering performance for the gene expression model. Then the filter gain is characterized in terms of the solution to a set of LMIs, which can easily be solved by using available software packages. A simulation example is exploited for a gene expression model in order to demonstrate the effectiveness of the proposed design procedures.