On Modeling and State Estimation for Genetic Regulatory Networks With Polytopic Uncertainties

It is widely believed that gene expression data contains rich information that could discover the higher-order structures of an organism and even interpret its behavior. The modeling problem of gene regulatory networks (GRNs) from the experimental data has recently received increasing research attention. In this paper, we investigate the uncertainty quantification and state estimation issues. The polytopic uncertainty model (PUM) is exploited for describing the GRNs where the parameter uncertainties are constrained in a convex polytope domain. To cope with the high-dimension problem for GRN models, the principal component plane (PCP) algorithm is proposed to construct a pruned polytope in order to use as less vertices as possible to maintain the essential information from original polytope. The so-called system equivalence transformation is developed to transform the original system into a simpler canonical form and therefore facilitate the subsequent state estimation problem. For the state estimation problem, a robust stability condition is incorporated with guaranteed H₂ performance via the semi-definite programme method, and then a new sufficient condition is derived for the desired H₂ estimators with several free slack matrices. Such a condition is vertex-dependent and therefore possesses less conservatism. It is shown, via simulation from real-world microarray time-series data, that the designed H₂ estimators have strong capability of dealing with modeling and estimation problems for short but high-dimensional gene expression time series.